MTH 302,FAQ`s BY CH SALMAN RASUL JATTALA

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1 Why Chi-square(c2) distribution is negatively skewed? One fundamental question in probability and statistical analysis is whether or not a pattern of observed data fits a given distribution such as a uniform, binomial, or normal distribution or some other distribution. Clearly, the data would not fit the distribution exactly, so we would want to have some criteria of GOODNESS of FIT. The chi-square distribution gives such criteria. In doing so this distribution is not symmetric and is skewed to the right. However for large value of its degree of freedom it can be close to normal distribution. What are lottery-style probabilty calculations?can probability help to win at gambling? Probability theory is, of course, used in gambling or lottery but it cant HELP you to win at gambling. Actually, mathematicians began studying probability as a means to answer questions about gambling games but not about its winnings. Besides gambling, probability theory is used in many other areas such as insurance, investing, weather forecasting, genetics, and medicine, and in everyday life. Probability can be called the mathematics of chance. The theory of probability is unusual in the sense that we cannot predict with certainty the individual outcome of a chance process such as flipping a coin or rolling a die (singularfor dice), but we can assign a number that corresponds to the probability of getting a particular outcome. For example, the probability of getting a head when a coin is tossed is 1/2 and the probability of getting a two when a single fair die is rolled is 1/6. But at the same time, it is a fact that we can also predict with a certain amount of accuracy that when a coin is tossed a large number of times, the ratio of the number of heads to the total number of times the coin is tossed will be close to 1/2. It is called the classical version of probability, which is often used in lottery. What is the dispersion of data? The data values in a sample are not all the same. This variation between values is called dispersion. When the dispersion is large, the values are widely scattered; when it is small they are tightly clustered. The width of diagrams such as dot plots, box plots, stem and leaf plots is greater for samples with more dispersion and vice versa. There are several measures of dispersion, the most common being the standard deviation. These measures indicate to what degree the individual observations of a data set are dispersed or 'spread out' around their mean. In manufacturing or measurement, high precision is associated with low dispersion. What is unique point,no point,infinite points solution of linear equation? You know very well that ax+b= (1) represents equation of a straight line parallel to y-axis. Now for such lines we see these three cases; 1) Unique point solution: If we have say a=3 and b=2 then eq:(1) becomes 3x+2=0 It gives x = -2/3 which is the case of unique of solution. It represents a straight line parallel to a y-axis and located to its left at unit of (-2/3) 2) No point solution: If we have a = 0 and b= 3 say then eq: (1) becomes 0(x) + 3 = 0 0x = -3 It is invalid(unlawful) equation as you can see on the left hand side, whatsoever value of x you have, we can never get -3 i-e the right hand side. So in this case we say that equation has no solution as there exists NO number in mathematics whose product with zero can give -3 3) Infinite many solution: For a=0 and b=0 in eq: (1), we have 0(x)+0 = 0 it gives 0(x) =0 It is valid (lawful) equation as you can see that ANY(even infinite many values) value of x can satisfy this. So it means equation is has infinte many solutions as EVERY number in mathematics multiplying by zero gives zero. Why interquartile range(iqr) is not affected by extreme values? IQR usually gives more accurate description of dispersion than the range. As the range may be strongly influenced by a single small or large value. Consider the following two lists for n = 7 ListA: 7,9,9,10,10,11,14 ListB: 7,7,8,10,11,13,14 For lista: Min = 7, Q1= 9, M=10, Q3=11, Max=14 So range = Max Min = 14-7 = 7 IQR = Q3-Q1 =11-9 = 2 For listb: Min = 7, Q1= 7, M=10, Q3=13, Max=14 So range = Max Min = 14-7 = 7 IQR = Q3-Q1 =13-7= 6 Here you can see that listb exhibits more dispersion than lista, The range of both lists are same. However IQR = 6 of listb is much larger than the IQR= 2 of lista. What is Correlation? Correlation The degree to which two variables are associated. For example, height and weight have a moderately strong positive correlation. What is the difference between NORMDIST and NORMSDIST. NORMDIST returns the normal distribution for the specific mean and standard deviation whereas NORMSDIST returns the normal distribution for mean =0 and standard deviation =1 What is the syntax and use of NORMINV function. NORMINV returns the inverse of normal cumulative distribution with the specified mean and standard deviation. Its syntax is NORMINV(probability,mean,standard_dev) For the input of NORMINV(0.5,1,-1) the system returns the # value! Error value.why? In the above formula the input for standard deviation is -1 i.e negative. Whereas standard deviation is always positive. What is standard error of the mean for the sample for which s=15, n=64 STEM=S.D/n^(1/2) =15/(64)^(1/2) =15/8 =1.875 To what limits of percentage the 95% confidence interval lies. 95% confidence interval for percentage is calculated as P +/- 2STEP Where P is percentage and STEP is standard error of percentage. Calculate the 95% confidence interval for percentage for the sample of 60 students which contain 12 (20%) who are left handed. Range = P +/- 2STEP =20 +/- 2[20*80/60]^(1/2) =20 +/- 2[5.164] =20 +/ = , =30.33 and 9.67 What is the probability that if we take a random sample of 64 children from a population whose mean IQ is 100 with a StDev of 15,the mean IQ of the sample will be below 95? 1

2 S=15;n=64; population mean=100 STEM=15/(64)^1/2 =15/8 =1.875 Z=(100 95)/STEM =5/1.875 =2.67 From normal probability the corresponding probability is which is quite low. An inspector took a sample of 100 tins of beans. The sample weight is 225g.Standard deviation is 5g.Calculate the 95% confidence interval for the population mean. STEM=s.d/(n)^1/2 Since s.d of population is not known,therefore we use s.d of sample as an approximation to s.d of population which is 5. Hence, STEM=5/(100)^1/2 =5/10 =0.5 95% confidence interval=225 +/- 2* 0.5 =225 +/- 1 = 225+1,225-1 =226,224 What is finite population correction factor and when it is used? If population is very large as compared to the sample then multiply STEM and STEP by Finite Population Correction Factor =[1-(n/N)]^1/2 Where N=Size of population. n=size of sample n=less than 0.1N What are type I and type II errors. Type I error occurs when we might conclude there is a significant difference while there is actually no difference. Type II error occurs when we might conclude that there is no significant difference while there is a significant difference. When do we use the 1_tailed and 2_tailed tests? One tail test is used when alternative hypothesis contains only one of the symbols of inequality (<,>) and does not contain the symbol?.two tailed tests are used when alternative hypothesis contains the symbol?. How do we decide that a specific hypothesis should be taken as null or alternative hypothesis? Null hypothesis is built in such a way that some probability distribution could be attached to that hypothesis.it usually contains the sign of equality whereas an alternative hypothesis does not contain the sign of equality. What is the syntax and use of CHITEST function. CHITEST returns the value from Chi_squared distribution for the statistic and appropriate degrees of freedom. Syntax CHITEST(actual_range,expected_range) Actual_range is the range of data that contains the observations to test against expected values. Whereas expected_range is the range of data that contains the ratio of product of row totals and column totals to the grand totals. What is PV function? PV is an Excel function that returns the present value of an investment. What is FV function? FV is an Excel function that returns the future value of an investment. What is NPV? NPV function returns the net present value of an investment based on a series of periodic cash flows and a discount rate. What is XNPV? XNPV returns the net present value for a schedule of cash flows that is not necessarily periodic. What is difference between NPV and XNPV? NPV is used to calculate present value of periodic cash flow, whereas XNPV is used to calculate present value of cash flow which is not periodic. How can the date be written in Excel? For writing date in Excel, you can use DATE function. Its syntax is as follows: =date( year, month, day) For example, if you want to write December 25, 2009, you can write it as: =date(2009, 12, 25) What is SLN? SLN is an Excel function which returns the straight-line depreciation of an asset for one period. What is SYD? SYS is an Excel function which returns the sum-of-years' digits depreciation of an asset for a specified period. What is VDB? VDB is an Excel function which returns the depreciation of an asset for any period you specify, including partial periods, using the double-declining balance method or some other method you specify. VDB stands for variable declining balance. What is IRR? IRR is an Excel function which Returns the internal rate of return for a series of cash flows represented by the numbers in values. These cash flows do not have to be even, as they would be for an annuity. However, the cash flows must occur at regular intervals, such as monthly or annually. The internal rate of return is the interest rate received for an investment consisting of payments (negative values) and income (positive values) that occur at regular periods. What is XIRR? XIRR is an Excel function which Returns the internal rate of return for a schedule of cash flows that is not necessarily periodic. What is a linear equation? A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. For example, 2x + 5y = 8 What are applications of linear equation in business? 2

3 Followings are the applications of linear equation in the field of business. Perform linear Cost-Volume-Profit and breakeven analysis employing: The contribution margin approach The algebraic approach of solving the cost and revenue functions What is Break-even point? It is the point at which no profit is made and no losses are incurred on that product. In other words, cost and revenue become equal. How is Break-even point expressed? Break even point can be expressed as 1. units 2. Sales or Rupees (Rs) 3. Percent of capacity What is the fixed cost? Fixed Costs are such costs that do not change if sales increase or decrease e.g. rent, property taxes, some forms of depreciation. What is variable cost? Variable costs change in direct proportion to sales volume e.g. material costs and direct labor costs. What is production capacity? It is the number of units which a firm can make in a given period. What is Contribution Margin? Contribution Margin is the Rs. amount that is calculated by deducting Variable Costs from Sales or revenues and contributes to meeting Fixed Costs and making a Net Profit. It can be calculated on a total or per unit basis. Contribution Margin = Net Sales Variable Cost = S VC What is Binomial? Binomial A polynomial with two terms which are not like terms. The following are all binomials: 2x 3, 3x5 +8x4, and 2ab 6a2b5. What is linear equation? A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one, two, three or more variables. An equation consists of Variables and Constants. Variables are denoted by x, y, z etc and Constants are denoted by 1,2,3 etc. For example, 2x +3=5, In this equation x is variable and 2,3,5 are constants. A linear equation is one in which degree of the equation is 1.Degree of the equation is determined by the power of the variable involved in the equation. For Example 3x+4=2 is a linear equation, because the power of x in this equation is 1.Also 4x+5y=1 is a linear equation, because degree of variables x and y is 1. Why we use Annuity? Define annuity. At some point in your life you may have had to make a series of fixed payments over a period of time - such as rent or car payments - or have received a series of payments over a period of time, such as bond coupons. These are called annuities. Annuities are essentially series of fixed payments required from you or paid to you at a specified frequency over the course of a fixed period of time. An annuity is a type of investment that can provide a steady stream of income over a long period of time. For this reason, annuities are typically used to build retirement income, although they can also be a tool to save for a child s education, create a trust fund, or provide for a surviving spouse or heirs. The most common payment frequencies are yearly (once a year), semi-annually (twice a year), quarterly (four times a year) and monthly (once a month). The term annuity is used in finance theory to refer to any terminating stream of fixed payments over a specified period of time. This usage is most commonly seen in academic discussions of finance, usually in connection with the valuation of the stream of payments, taking into account time value of money concepts such as interest rate and future value. Examples of annuities are regular deposits to a savings account, monthly home mortgage payments and monthly insurance payments. Annuities are classified by payment dates. The payments (deposits) may be made weekly, monthly, quarterly, yearly, or at any other interval of time. Payment made at a fixed interval. A common example is the payment received by retirees from their pension plan. There are two main classes of annuities: annuities certain and contingent annuities. Under an annuity certain, a specified number of payments are made, after which the annuity stops. With a contingent annuity, each payment depends on the continuance of a given status; for example, a life annuity continues only as long as the recipient survives. Contingent annuities such as pension plans or life insurance depend on shared risk. Everyone pays in a fixed amount until the annuity begins; some will not live long enough to receive back all the money they have paid, while others will live long enough to collect more than they have. What is Accumulation Factor? Accumulated value means that the total amount of the money which you will get after a specific period of time of your investment. Or Accumulated value means how much your money's worth after it earns interest or experiences capital growth. Includes the amount you started with, plus any increase. Accumulated value = payment*accumulation factor For example if you invest 100 Rs for one year at a profit rate of 10% then the accumulated value will be 110 Rs after one year. The Accumulation Factor can be calculated by treating the value at the end of year. In this example, the accumulation factor after year 1 is /100=1.1.The accumulation factor after year 2 will be /100=1.21. So formula for accumulated value is S = r ((1+i)^n-1/i Where, S is accumulated value, I is interest rate per conversion period, n is number of payments and r is amount of annuity. what is meant by compounding period and nominal interest rate in effect function? The compounding period is length of time over which interest on an investment is calculated The nominal interest rate is the actual interest rate quoted by financial lenders and others. It is the stated rate of interest to be paid on a loan. The rate the 3

4 lender says the borrower will pay, it can be either a flat or declining balance rate. Nominal interest rates shows little about the costs of a loan. What is the major Difference between pmt and ppmt.? PMT Returns the periodic payment for an annuity. PMT (rate,nper,pv,fv,type) Rate: interest rate Nper: total number of payments Pv: present value Fv: future value Type: number 0 (zero) or 1 PPMT Returns the payment on the principal for an investment for a given period. PPMT (rate,per,nper,pv,fv,type) Rate: interest rate per period. Per: period and must be in the range 1 to nper Nper: total number of payment periods Pv: the present value Fv: future value (0) Type: the number 0 or 1 (due) PMT& PPMT have different formulae Explain the Term "CUMPRINC". CUMPRINC returns the cumulative principal paid on a loan between start_period and end_period. Syntax CUMPRINC(rate,nper,pv,start_period,end_period,type) Rate is the interest rate. Nper is the total number of payment periods. Pv is the present value. Start_period is the first period in the calculation. Payment periods are numbered beginning with 1. End_period is the last period in the calculation. Type is the timing of the payment. Type Timing 0 (zero) Payment at the end of the period 1 Payment at the beginning of the period What is Cumipmt? CUMIPMT is an Ms excel financial function which returns the cumulative interest paid between two periods i.e. to calculate the interest paid on a loan between start_period and end_period. Its syntax or formula is CUMIPMT(rate,nper,pv,start_period,end_period,type) Rate is the interest rate. Nper is the total number of payment periods. Pv is the present value. Start_period is the first period in the calculation. Payment periods are numbered beginning with 1. End_period is the last period in the calculation. Type is the timing of the payment. Type Timing 0 (zero) Payment at the end of the period 1 Payment at the beginning of the period If you want to know more about this function then go to Ms Excel help and write this function. You will get enough information about this function. What is multiplicative identity? In order to understand multiplicative inverse and identity let us consider the example of numbers. The number 1 is called the identity as it satisfies the following: 1.b = b.1 = b for any real number b. In case of matrices the identity matrix plays the role of the multiplicative identity. what are excel Matrix Functions? A Matrix is a rectangular array of numbers. while doing with matrices we may be interested in multiplication of matrices, determinant of a matrix,inverse of a matrix.these all are called matrix functions and in Microsoft excel we have functions to compute these all,so The Matrix Functions in Microsoft Excel are as follows: 1. MINVERSE 2. MDETERM 3. MMULT What is the difference between Array and Dimension? Arrays are the number in specific sequence while the dimension is the number of rows & columns in matrix. e.g: a matrix having three rows & four columns then its dimension is represented by " 3*4 ": Is AxB =Bx A in matrix multiplication or not if are not then why? When the number of columns of the first matrix is the same as the number of rows in the second matrix then matrix multiplication can be performed. Here is an example of matrix multiplication for two 2x2 matrices A 2x2 matrix cannot be equal to a 3x3 matrix as they don't even have the same number of elements (let alone all the corresponding elements having to be equal). So in that case AxB certainly does not equal BxA. A B? B A let A = [1 2] [3 4] let B = [5 6] [7 8] A B = [19 22] [43 50] B A = [23 34] [31 46] Note: That AxB is not the same as BxA Define multiplicative inverse for matrix. If X is any set with multiplications * defined on it and a is any element of X then the multiplicative inverse of a is another element of X notated by a-1 such that a* a-1 = a-1 *a =e Where e is the multiplicative identity of X. For example the multiplicative inverse of 4 in R is 1/4 because 4(1/4) = (1/4) 4 = 1 Where 1 is the multiplicative identity of R. Similarly the inverse of a square matrix A is another square matrix B of the same order such that AB = BA = I Where I is the multiplicative identity of matrices. Explain the Identity Matrix. The multiplicative identity matrix is the square matrix which when multiplied by any other square matrix of the same order does not disturbs its identity i.e., If A is a square matrix and I is the identity then AI = IA = A In this respect the matrix I, which has only real number 1 as its principal diagonal and zeros elsewhere, is the only square matrix that satisfies the above definition. in identity matrix diagonal element = 1. Define the term Frequency: The number of times that an event occurs within a given period. Define the term Cumulative Frequency: The cumulative frequency is the running total of the frequencies. We sum up all the previous frequencies. Example: Height (cm) Frequency Cumulative Frequency (= 4 + 6) (= ) (= ) How we find Percent Relative Frequency? Percent Relative Frequency of a class =[Frequency of the class interval/total frequency] *100 How we find the Arithmetic mean of grouped data? Arithmetic mean of grouped data = Sum of (f*x)/ sum of (f) What you ll infer about a population divided by its median provided that if its two halves contain less than half the 4

5 population? At most half the population have values less than the median and at most half have values greater than the median. If both halves contain less than half the population, then some of the population is exactly equal to the median. Describe the quantitative role of mean and median under the concept of skewness? The mean is typically higher than the median in positively skewed distributions and lower than the median in negatively skewed distributions. Is there is any arithmetic formulation for calculating the mode of a statistical data? For a given set of values, mode may not be a single value. It cannot be calculated arithmetically and one has to compare all the values to obtain the modal value. It only tells us about the most frequent value and does not take into account the remaining values or their frequencies. Explain the use of matrix and determinants and in which feilds? also tell its origion and importance. The beginnings of matrices goes back to the second century BC although traces can be seen back to the fourth century BC. However it was not until near the end of the 17th Century that the ideas reappeared and development really got underway. It is not surprising that the beginnings of matrices and determinants should arise through the study of systems of linear equations. The Babylonians studied problems which lead to simultaneous linear equations and some of these are preserved in clay tablets which survive. The Chinese, between 200 BC and 100 BC, came much closer to matrices than the Babylonians. Matrices are used to solve problems in electronics,statics,robotics,linear programming,optimisation,intersections of planes,genetics and we can use the determinant of a matrix to solve a system of simultaneous equations. Define COUNT function: Excel's COUNT function is one of a group of Count Functions that can be used when you need to total the number of cells in a selected range. Use it when you want to count how many numbers are there in a selected range. How we can multiply one matrix to othr matrix in the excel? For multiplication of matrices, you can use the "MMULT" function. It can be used by following the steps written under. 1- Select the range of cells where your answer will be displayed. 2-Press F2 from your key board. 3-Write the syntax of the function as "=MMULT(array1,array2)" array1 is the first matrix and array2 is the second matrix. 4- Press "Ctrl+Shift+Enter", your answer will be displayed on the selected range what is the importance of matrices in business? In business you know linear programming is very important.in linear programming you always try to get maximum profit with minimum cost and in linear programming you use matrices also to make calculations without sketching because without using matrices you have to sketch each and every thing which is tiresome.dear student if you find any difficulty you can contact me again. what is the importance of matrices in business? In business you know linear programming is very important.in linear programming you always try to get maximum profit with minimum cost and in linear programming you use matrices also to make calculations without sketching because without using matrices you have to sketch each and every thing which is tiresome.dear student if you find any difficulty you can contact me again. Define "Asset Value". Asset Value is a net market value of a company's assets on a per-share basis as opposed to the market value of the shares. A company is undervalued by the stock market when asset value exceeds share value. Why we use semi colon";" in the formula of round? can i use coma(,) instead of semi colon? Most of the excel versions are using the concept of "Coma" instead of "Semi Colon" You can use any of them according to your version of software. What is the difference between + and : because in some formulas is is used : instead of + If you use SUM function then : will be used otherwise +. Explain about payroll. The term 'payroll' encompasses every employee of a company who receives a regular wage or other compensation. Some employees may be paid a steady salary while others are paid for hours worked or the number of items produced. All of these different payment methods are calculated by a payroll specialist and the appropriate paychecks are issued. Companies often use objective measuring tools such as timecards or timesheets completed by supervisors to determine the total amount of payroll due each pay period. Certain life events may affect your pay or deductions, causing them to stop, restart, increase, or decrease. Various policies, forms, and fiscal procedures have been developed to address these life events. These include benefits changes (Benefit Life Events). Tell about round formula. ROUND function is used to display the answer up to the desired decimal places. Syntax ROUND(number,num_digits) Number is the number you want to round. Num_digits specifies the number of digits to which you want to round number. 5

6 For example =ROUND(2.5497, 0) rounds to an integer. (Answer is 3) =ROUND(2.5497,1) rounds to one decimal place.(answer is 2.5) =ROUND(2.5497,2) rounds to two decimal places.(answer is 2.55) By this function, you can get as much precise answer as you want. What is the purpose of(=round)? Rounding is a method to approximate a number to a certain place. Sometimes we get a very large number or decimal number with many digits. We want to cut short its some digits up to suitable approximated number without disturbing actual value. Suppose, there is number While displaying it, we make it short without disturbing its main value. We can write it as It is suitable form and easy to understand. Why $ is used in cell references? In excel the alphabet in cell reference indicate column and the preceding number indicate the row. For example A23 refers to cell in A column and 23rd row. The $ sign is used before the row or column reference to fix the location of the cell. If $ sign come before column reference, it is called absolute column. If $ sign comes before row reference, it is called absolute row. The column reference and row reference without $ sign is called relative column reference and relative row reference. There are four types of cell references. 1. Absolute column and absolute row reference. It is simply called absolute cell reference. For example $A$23 2. Relative column and absolute row reference. For example A$ Absolute column and relative row reference. For example $A Relative column and relative row reference. For example A23. What is Exponential Smoothing? Exponential Smoothing assigns exponentially decreasing weights as the observation get older. In other words, recent observations are given relatively more weight in forecasting than the older observations what is Statistical Representation of Data? Statistical Representation of Data: Because a list of raw data may be difficult to interpret, statisticians prefer to represent their data in an organized way. Such arrangement of data is called Statistical Representation of Data. Two of the most common ways to arrange the data are frequency distributions and graphs. What is Factorial? Factorial The product of a given integer and all smaller positive integers. The factorial of n is written n! and is read aloud "n factorial". Note: By definition, 0! = 1. define 6!. 6! = = 720 What is the difference between sd and md? A simple deviation is difference or movement away from a standard. It is the difference between a number and the average of a set of values. The standard deviation measures the spread of the data about the mean value. It is useful in comparing sets of data which may have the same mean but a different range. For example, the mean of the following two is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. However, the second is clearly more spread out. If a set has a low standard deviation, the values are not spread out too much. What is the purpose of knowing variance and standard deviation? Variance is basically a measure of the general dispersion of data in a sample, it gives you a sense of how far away data points are from one another. the larger the variance, the more variability you have in your sample. Standard deviation is more concrete: it is the average distance of each point in the sample from the sample mean in terms of the original units of measurement. for instance, say you want to estimate the average height of a high school male basketball player. you take a sample of 10 varsity basketball players from your school and calculate their height and standard deviation. say you find that the mean of the sample is 70 in with a standard deviation of 2, you can say that the average difference between any given high school varsity basketball player is 2 inches from the mean of 70. it gives you a tool for making educated predictions about a population. if your sample is normally distributed, you can make even more educated predictions; in a normal distribution, 68% of the population falls between -1 and +1 standard deviations (from the mean), 95% of the population falls between - 2 and +2 SD, and approximately 99% of the population falls between - 3 and +3. What is variance? Variance is how your results variates from your expected value or win rate. If that wasn't simple enough: It's how bad/good you can run. When do we use correlation? It will be used when we wish to establish whether there is a degree of association between two variables. If this association is established, then it makes sense to proceed further with regression analysis. Regression analysis determines the constants of the regression. You can not make any predictions with results of correlation analysis. Predictions are based on regression equations. Discuss the contribution of correlation analysis in the different fields? Correlation analysis contributes to the understanding of economics behavior, aids in locating the critically important variables on which others depends, may reveal to the economist the connections by which disturbances spread and suggest to him the path through which stabilizing forces may become effective. Describe the simaltanous contrast of regression and correlation? Correlation deals with the association (importance) between variables whereas regression deals with prediction (intensity). What is the usage of intercept function? Use the INTERCEPT function when you want to determine the value of the dependent variable when the independent 6

7 variable is 0 (zero). For example, you can use the INTERCEPT function to predict a metal's electrical resistance at 0 C when your data points were taken at room temperature and higher. How we can use analysis tool pack? You can use EXCEL to perform a statistical analysis: On the Tools menu, click Data Analysis. If Data Analysis is not available, load the Analysis ToolPak. In the Data Analysis dialog box, click the name of the analysis tool you want to use, and then click OK. In the dialog box for the tool you selected, set the analysis options you want. You can use the Help button on the dialog box to get more information about the options. Explain some valid and invalid features of slope functions? 1) The arguments must be numbers or names, arrays, or references that contain numbers. 2) If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included. 3) If known_y's and known_x's are empty or have a different number of data points, SLOPE returns the #N/A error value. What is binomial coefficients? A binomial coefficient equals the number of combinations of r items that can be selected from a set of n items. It also represents an entry in Pascal's triangle. These numbers are called binomial coefficients because they are coefficients in the binomial theorem. Define Permutation. A selection of objects in which the order of the objects matters. Example: The permutations of the letters in the set {a, b, c} are: abc acb bac bca cab cba Define Combination. Combination Formula A formula for the number of possible combinations of r objects from a set of n objects. This is written in any of the ways shown below. ncr or C(n,r) = n!/(r!(n-r)!) All forms are read aloud "n choose r." Example: How many different committees of 4 students can be chosen from a group of 15? C(15,4) = 1365 Define the term Mean: The sum of a list of numbers, divided by the total number of numbers in the list is called a mean. Define the term Median: "Middle value of a list. The smallest number such that at least half the numbers in the list are no greater than it. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle (after sorting) numbers divided by two. Define the term Mode: For lists, the mode is the most common (frequent) value. A list can have more than one mode. A data set has multiple modes when two or more values appear with the same frequency. What is range of data? Range = Maximum value Minimum Value What is Relative frequency? Relative Frequency of a class = Frequency of the class interval/total Frequency What is margin? A ratio of profitability calculated as net income divided by revenues, or net profits divided by sales. It measures how much out of every dollar of sales a company actually keeps in earnings. Profit margin is very useful when comparing companies in similar industries. A higher profit margin indicates a more profitable company that has better control over its costs compared to its competitors. Profit margin is displayed as a percentage; a 20% profit margin, for example, means the company has a net income of $0.20 for each dollar of sales. Also known as Net Profit Margin. What is the formula for markup on sale? Markup on sale = (Selling price - Cost price/selling Price) 100% What is the formula for markup on cost? Markup on cost = (Selling price Cost price)/(cost price) 100% What is Binomial Distribution? Binomial probability distribution arises in any situation where there are: (1) only two possible outcomes, (2) the number of trials or observations is fixed, (3) all the observations are independent 4) the probability of a success (p) is identical for each observation. In the binomial situation the letter p stands for the probability of a success. Before it has just stood for the word probability. In the binomial situation q is used to designate the probability of a failure. Success and failure are difficult words to define at times within these problems. Just remember that there are only two possible outcomes in these situations. One situation might be coded with a one (1) while the other is coded with a zero (0). For example, you might answer a question on a test correctly (pass) and receive one point, or answer the question incorrectly (fail) and receive zero points. P would indicate the probability of getting a one and q would indicate the probability of getting a zero. On any event, p + q must always equal 1. You must do one or the other if there are only two possible outcomes. As has been our custom, we work a problem before presenting the formulas. To compute a binomial probability, you need to calculate and multiply three separate factors: the number of ways to select exactly k successes, the probability of success (p) raised to the k power, and the probability of failure (q) raised to the (n-k) power. Since success and failure are the only two possibilities, q = 1 - p. The probability of k successes in a binomial(n,p) distribution is: P(x=k) = n! / (k!(n-k)!) * p^k * q^(n-k) 7

8 Explain Cumulative Binomial Distribution. Cumulative probability is very useful in finding the probability of an occurrence that cannot be predictable in a specified range. The idea of the random variable is used for it. It is a variable whose values are numerical events that cannot be predicted with certainty. Define slope. y = mx + b, where m is the slope and b is the y-intercept. Slope-intercept is the form used most often as the simplified equation of a line. Define Null Hypothesis. The null hypothesis, H0, represents a theory that has been put forward, either because it is believed to be true or because it is to be used as a basis for argument, but has not been proved. For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current drug. We would write H0: there is no difference between the two drugs on average. What is Confidence Level? Confidence Level The confidence level is the probability value (1-alpha) associated with a confidence interval. It is often expressed as a percentage. For example, say alpha=0.05, then the confidence level is equal to (1-0.05) = 0.95, i.e. a 95% confidence level. Define Confidence limits. Confidence limits are the lower and upper boundaries / values of a confidence interval, that is, the values which define the range of a confidence interval. Under which condition the mean and median of a data are equal? If a data consists of only two terms then the mean = average (mean) On the histogram, how you can locate the median? Geometrically the median is the value of X (abcissa) corresponding to the vertical line which divide a histogram into two parts having equal areas. How you can locate median on the ogive curve(cumulative frequency curve)? On the ogive curve, the median is the abscissa of point P whose ordinate is 50%. With the help of an example justify that the sum of squared deviations of the mean is less than the median? The numbers 1, 2, 3, 7, 8, 9, 12 have a mean of 6 and median of 7. The mean minimizes sum of squared deviations. The sum of the squared deviations from the mean is: (1-6)² + (2-6)² + (3-6)² + (7-6)² + (8-6)² + (9-6)² + (12-6)² = = 100. From the median: (1-7)² + (2-7)² + (3-7)² + (7-7)² + (8-7)² + (9-7)² + (12-7)² = = 107 Justify with the help of an example that the sum of absolute deviations of the median is less than mean? The numbers 1, 2, 3, 7, 8, 9, 12 have a mean of 6 and median of 7. The sum of the absolute values of the deviations from the mean are: Abs(1-6)+ Abs(2-6)+ Abs(3-6)+ Abs(7-6)+ Abs(8-6)+ Abs(9-6)+ Abs(12-6) = = 24. From the median: Abs(1-7)+ Abs(2-7)+ Abs(3-7)+ Abs(7-7)+ Abs(8-7)+ Abs(9-7)+ Abs(12-7) = = 23. Define Qualitative Data: Qualitative data is extremely varied in nature. It includes virtually any information that can be captured that is not numerical in nature, e.g. Sex, religion. Define quantitative data : Information that can be counted or expressed numerically. This type of data is often collected in experiments, manipulated and statistically analyzed. Quantitative data can be represented visually in graphs and charts, e.g. Heights, weights, incomes etc. Write down the types of graphs: 1 Picture graph 2 Column Graphs 3 Line Graphs 4 Circle Graphs (Sector Graphs) 5 Conversion Graphs 6 Travel Graphs 7 Histograms 8 Frequency Polygon 9 Cumulative Polygon or Ogive Under which condition measure of dispersion of data is zero or greater or less than zero? A measure of statistical dispersion is a real number that is zero if all the data are identical, and increases as the data becomes more diverse. It cannot be less than zero. Give the description about the scale or unit of the measure of dispersion? Most measures of dispersion have the same scale as the quantity being measured. In other words, if the measurements have units, such as metres or seconds, the measure of dispersion has the same units. Enlist some scale free measure of dispersion? Some measures of dispersion which are dimensionless (scale-free) that is they have no units even if the variable itself has units. These include: 1) Coefficient of variation 2) Quartile coefficient of variation 3) Relative mean difference Define absolute measure of dispersion? It is the dispersion in terms of the same units as the unit of the data. For example if the units of the data are in cm, liter or kg the unit of measures of dispersion is also in cm, liter or kg.the commonly used absolute dispersion is range, quartiles, mean deviation, standard deviation, and variance. 8

9 Discuss the ineligibility of the use of absolute measure of dispersion? Absolute dispersion cannot be used to compare the variation in two or more than two sets of data. Define relative measure of dispersion? A measures of dispersion when expressed as pure number in the form of a coefficient, percentage or ratio is called relative measures of dispersion. The relative measures of dispersion are coefficient of range, coefficient of quartile deviation, mean coefficient of dispersion, coefficient of variation. Discuss the eligibility of the use of relative measure of dispersion? Since absolute measures of dispersion are independent of unit of measurement, therefore can be used to compare the variation between two or more then two sets of data. Shortly discuss the characteristics of different commonly used means? 1) The arithmetic mean and represents the overall average. 2) The median divides data in two equal parts. 3) Mode is the most common value. 4) Geometric mean is used in compounding such as investments that are accumulated over a period of time. 5) Harmonic mean is the mean of inverse values. Which is the best measure of central tendency and why? The best of tendency is arithmetic mean. It is defined as a value obtained by dividing the sum of all the observation by their number, that is mean = [sum of all the observations]/[number of the observations] Arithmetic mean is used because it is simple to understand and easy to interpret. It is quickly and easily calculated. It is amenable to mathematical treatments. It is relatively stable in repeated sampling experiments. Describe the significance of central tendency? The term central tendency refers to the middle value or perhaps a typical value of the data, and is measured using mean, median or mode.each of these measures is calculated differently, and the one that is the best to use depends upon the situation. Explain the limitations of Arithmetic mean? The mean is a fine measure of central tendency for approximately symmetric distributions but can be ambiguous in distorted distributions, since it can be greatly prejudiced by scores in the tail. Therefore, other statistical tools like the median may be more informative for distributions such as family income or reaction time that are frequently very skewed. What is an outlier? An outlier is an observation in a data set which is far removed in value from the others in the data set. It is an unusually large or an unusually small value compared to the others. For a set of numerical data, any value that is markedly smaller or larger than other values. For example, in the data set {3, 5, 4, 4, 6, 2, 25, 5, 6, 2} the value of 25 is an outlier. An outlier might be the result of an error in measurement, in which case it will distort the interpretation of the data, having undue influence on many summary statistics, for example, the mean. If an outlier is a genuine result, it is important because it might indicate an extreme of behaviour of the process under study. For this reason, all outliers must be examined carefully before embarking on any formal analysis. Outliers should not routinely be removed without further justification. Which is the measure of central tendency that is most affected by outliers? Imagine a set of numbers, {1, 5, 5, 5, 10}. The mean is ( )/5 = 5.2. This is the common "average" that people usually talk about--add up all of the numbers, and then divide by how many there are. The median is 5. You take the middle number in the entire group. The mode is 5. It's simply the most common value in the set. The range here is 10-1 = 9, however. This is the only measure that is listed that is drastically affected by the outliers! If we took a similar set, {4, 5, 5, 5, 7}, with a closer grouping of values, the mean, median, and mode remain the same. The range changes to 7-4 = 3, however. Keep in mind that if the outliers are not evenly distributed to both sides of the set, the mean can end up being drastically different, as well, especially if they are significantly larger or smaller than the other numbers in the group. However, the median and mode are unlikely to change. Define Trend. Trend is a long term movement in a time series. It is the underlying direction (an upward or downward tendency) and rate of change in a time series, when allowance has been made for the other components. Define Regression Equation. A regression equation allows us to express the relationship between two (or more) variables algebraically. It indicates the nature of the relationship between two (or more) variables. In particular, it indicates the extent to which you can predict some variables by knowing others, or the extent to which some are associated with others. A linear regression equation is usually written Y = a + bx + e where Y is the dependent variable a is the intercept b is the slope or regression coefficient X is the independent variable (or covariate) e is the error term What is residual? Residual Residual (or error) represents unexplained (or residual) variation after fitting a regression model. It is the difference (or left over) between the observed value of the variable and the value suggested by the regression model. What is the series discount? It is a further discount as incentives for more sales. Usually such discount is offered for selling product in bulk. If series discount of 16%, 20%, 15% are offered on list price, say L= Rs.20000, of an item then net price is calculated as follows: Let d1 = 16%, d2 = 20%, d3 = 15%, then above formula becomes N = L (1 d1)(1 - d2)(1 - d3) N = L (1 16%) (1 20%) (1 15%)= 20000*0.84*0.80*0.85 = Rs What is the cash discount? 9

10 A reduction in the price of an item for sale allowed if payment is made within a stipulated period. Such a discount is an advantage to both the seller and the buyer. The buyer has a saving of money while the seller has funds at his disposal. What is the discount period? The period during which a customer can deduct the discount from the net amount of the bill when making payment What are the credit periods? Credit Periods are periods for the buyers to pay invoices within specified times. What is the seasonal discount? Seasonal discount is the reduced price to encourage the purchase of a particular product in the off-season; perhaps better thought of as an "out-of-season" discount What is correlation coefficient? The correlation coefficient is a numerical way to quantify the relationship between two variables, e.g. X and Y and it is denoted by the symbol R. The correlation coefficient is always between -1 and 1, thus -1 < R < 1. If the correlation coefficient, R, is positive, then a increase in X would result in a increase in Y, however if R was negative, an increase in X would result in a decrease in Y. Larger correlation coefficients, such as 0.8 would suggest a stronger relationship between the variables, whilst figures like 0.3 would suggest weaker ones. However, the correlation coefficient does not imply causality, that is it may show that two variables are strongly correlated, however it doesn t mean that they are responsible for each other. What is negative binomial distribution? Negative Binomial Experiments: The experiments in which no. of success fixed and trails varies to produce the fixed no. of success called negative binomial experiments and its probability distribution function is P(X=x) =(x-1)c(k-1)*p^k *q^(x-k) ; x= k, k+1, It has two parameters k and p>0 Differentiate between Binomial and Negative Binomial Distribution. In binomial distribution the no. of trails are fixed and the success varies while in negative binomial distribution no. of success fixed and trails varies. What is Poisson Distribution? A limiting approximation of the binomial distribution when p, the probability of success is very small and n, the number of trails is so large the product mean= np is of moderate size. Mean= Variance is the only parameter of Poisson distribution What is Poisson is process? The Poisson process is a process in which the occurrence of events is noticed in a specified interval of time. If initial value =12 and final value = 15 Then find percentage change. Change = final value - initial value = = 3 Percentage change = (change/initial value) *100% = (3/12)*100% = 25% What is normal distribution? The limiting form of a binomial distribution by increasing the number of trails, to a very large number for a fixed value of p, the probability of success. It has two parameters mean and variance. Where, sigma = sqrt(variance) What is standardized normal variable? The standard normal variable is denoted by Z and defined as Z= (X- mean)/ sigma What is Standardized normal distribution? The normal probability distribution of normally distributed variable Z having zero mean and unit variance is called Standard normal distribution Define Correlation and types of Correlation. The word correlation or co-relation means a mutual relationship. It is the interdependences of two quantities variables. Although it has different types but here we describe only two 1) Positive correlation: If the values of variables are varying(ie increasing or decreasing) in the same direction then such correlation is referred to as positive correlation. e.g: there exist positive correlation b/w sales of soft drinks & temperature of surroundings because as the temperature of surroundings increases the sales of soft drinks also increases. Thus direction of varying of the sales & temperature is the same. 2) Negative correlation: If the values of variables are varying(i-e increasing or decreasing) in the opposite direction then such correlation is referred to as positive correlation. e.g: there exist negative correlation b/w pressure of gas & its volume because as the pressure is increased then volume is decreased. Thus direction of varying of volume & pressure is opposite. Other types are perfect + & perfect -, simple & zero correlation. Define Time series. Time Series: An arrangement of data by successive time periods is called a time series. What is Exponential smoothing? The Exponential smoothing is a type of weighted moving average forecasting technique in which past observations are geometrically discounted according to their age. The heaviest weight is assigned to the most recent datum. The smoothing is termed 'exponential' because data points are weighted in accordance with an exponential function of their age. Define Correlation Coefficient Correlation Coefficient A correlation coefficient is a number between -1 and 1 which measures the degree to which two variables are linearly related. If there is perfect linear relationship with positive slope between the two variables, we have a correlation coefficient of 1; if there is positive correlation, whenever one variable has a high (low) value, so does the other. If 10