Pearson LCCI Level 2 Certificate in Business Statistics (VRQ)

Transcription

1 Pearson LCCI Level 2 Certificate in Business Statistics (VRQ) (ASE20096) L2 SAMPLE ASSESSMENT MATERIALS For first teaching from January 2015

2 Mark Scheme Sample Assessment Materials Pearson LCCI Level 2 Certificate in Business Statistics (ASE20096)

3 LCCI Qualifications LCCI qualifications come from Pearson, the world s leading learning company. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. For further information, please visit our website at Pearson: helping people progress, everywhere Our aim is to help everyone progress in their lives through education. We believe in every kind of learning, for all kinds of people, wherever they are in the world. We ve been involved in education for over 150 years, and by working across 70 countries, in 100 languages, we have built an international reputation for our commitment to high standards and raising achievement through innovation in education. Find out more about how we can help you and your students at: All the material in this publication is copyright Pearson Education Ltd 2015

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5 General Marking Guidance All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last. Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions. Examiners should mark according to the mark scheme not according to their perception of where the grade boundaries may lie. There is no ceiling on achievement. All marks on the mark scheme should be used appropriately. All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, i.e. if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate s response is not worthy of credit according to the mark scheme. Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited. When examiners are in doubt regarding the application of the mark scheme to a candidate s response, the team leader must be consulted. Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response. Where marks are awarded for own figure answers, these marks can only be awarded if evidence of how the candidate arrived at their values has been provided (their workings). If candidates fail to provide their workings when instructed in the paper, it may not be possible to achieve all marks associated with the question, even if the final answer is correct. For calculation questions, full marks can be awarded where correct answer is seen with no workings shown, unless question states that candidate must provide workings. Pearson LCCI Level 2 Certificate in Business Statistics 1

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7 Write your name here Surname Other names Pearson LCCI Centre Number Candidate Number Certificate in Business Statistics Level 2 Sample assessment material for first teaching January 2015 Time: 2 hours 30 minutes Paper Reference ASE20096 You must have: statistical formulae sheet (enclosed), HB pencil, eraser Total Marks Instructions Use black ink or ball-point pen use a pencil to draw diagrams/graphs. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Answer the questions in the spaces provided there may be more space than you need. Answers should be given to an appropriate degree of accuracy. Information The total mark for this paper is 100. The marks for each question are shown in brackets use this as a guide as to how much time to spend on each question. A formulae sheet is provided at the front of the question paper. Calculators may be used. Advice Read each question carefully before you start to answer it. Try to answer every question. You are advised to show your workings. Check your answers if you have time at the end. Turn over S48185A 2014 Pearson Education Ltd. 1/ *S48185A0126* Pearson LCCI Level 2 Certificate in Business Statistics 3

8 ( Pearson LCCI Level 2 Certificate in Business Statistics Formula sheet Median for grouped data l cm m+ f m ( n 2 F m 1 where l m, c m and f m are the lower boundary, width and frequency respectively of the median class, n is the total number of observations and F m frequency corresponding to l m. 1 is the cumulative Mean for ungrouped data x Mean for grouped data x x f f x n Standard deviation for ungrouped data S Standard deviation for grouped data S f x 2 ( ) x f 2 n ( x x f f 2 ( 2 Quartile deviation Q 3 Q 1 2 Mean deviation f x mean f Coefficient of variation x s 100 Product moment correlation coefficient r n x y x y n x x n y y Spearman s rank correlation coefficient r s 1 6 d 2 1 n ( n 2 ) Least Squares regression line y a bx b a n x y x y n x 2 x 2 y b x n n Laspeyres index Paasche index Weighted index Price p 1 q 0 p q p 1 q 1 p q WI W Quantity p 0 q 1 p q p 1 q 1 p q Multiplication rule of probability P A Addition rule of probability P A ( if and independent B ) P ( A) P ( B ) A B ( B ) P ( A ) P ( B ) P ( A B ) *S48185A0226* 2 4 Pearson LCCI Level 2 Certificate in Business Statistics

9 Answer ALL questions. Write your answers in the spaces provided. 1 Businesses rely on data to help them function profitably. (a) Define the following types of data: (i) primary (ii) secondary. (b) Complete the table stating one example and one advantage for each source of data (primary and secondary). (4) Source Example Advantage Primary Secondary *S48185A0326* Pearson LCCI Level 2 Certificate in Business Statistics 3 5

10 The table below shows the breakdown of the costs of car fuel, as provided by a national retailer. Costs per litre Retailer margin Cost of refining Sales tax Cost of oil Duty 7.3 p 1.5 p 22.4 p 45.1 p 58.0 p The editor of a motoring magazine wants to represent this information using a pie chart. (c) Calculate the angles, representing this information in a pie chart for: (i) duty (ii) cost of refining. Sales tax and duty are government taxes. (d) Calculate, as a percentage, the cost of car fuel that is a government tax. *S48185A0426* 4 6 Pearson LCCI Level 2 Certificate in Business Statistics

11 The magazine editor also carried out research for a major motor insurance company. He found out information relating to the number of customers who were two weeks late in paying their accounts. 75% of customers owned their own cars, of these, 20% were late in paying their accounts. The remaining customers were companies, of these, 30% were late in paying their accounts. (e) Calculate the probability that an account selected at random will be: (i) held by a company and paid on time (ii) paid late. (3) *S48185A0526* Pearson LCCI Level 2 Certificate in Business Statistics 5 7

12 Two accounts are chosen at random. (f) Calculate the probability that both of these accounts are paid on time. (3) (Total for Question 1 = 20 marks) *S48185A0626* 6 8 Pearson LCCI Level 2 Certificate in Business Statistics

13 BLANK PAGE QUESTION 2 BEGINS ON THE NEXT PAGE. *S48185A0726* Pearson LCCI Level 2 Certificate in Business Statistics 7 9

14 2 A management consultancy company offers training courses. The Financial Director has investigated the cost of competing courses. The following data gives a summary of the costs of 120 similar courses. Cost of course ( ) Frequency 50 and up to and up to and up to and up to and up to and up to (a) Draw a cumulative frequency curve for the data, on the graph paper provided. (5) 10 Pearson LCCI Level 2 Certificate in Business Statistics

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16 12 Pearson LCCI Level 2 Certificate in Business Statistics *S48185A01026* (b) Use your cumulative frequency curve to estimate the: (i) median cost (ii) quartile deviation (4) (iii) percentage of courses that cost over 500.

17 (c) Explain one feature of the median that would make it a more suitable measure than the mean, when summarising the data. At the end of their courses, the management consultancy company asked a subgroup of delegates for feedback. Out of 120 delegates, they chose a sample of 10 by numbering the population from 1 to 120. A number between 1 and 12 was then selected at random. The number 5 was chosen and then delegates numbered 5, 17, 29, 41,,113 were included in the sample. (d) Name this sampling method. (e) State the sampling fraction used in selecting delegates from the population. (f) State one reason why the sampling method used might be unreliable. (g) State two advantages of face-to-face interviews (Total for Question 2 = 20 marks) *S48185A01126* Pearson LCCI Level 2 Certificate in Business Statistics 11 13

18 3 The Capital Tourist Company organises visits around the city of London s attractions and consequently its volume of business is dependent on the number of visitors to London from overseas. The following chart shows the total number of visitors (in thousands) to London from eight countries in 2003 and Chart Visitors (thousands) USA France Germany Italy Spain Country Netherlands Irish Republic Australia (Source: Crown copyright 2014) (a) Name the type of chart used to display the data. (b) State the country that had the larget increase in visitors to London between 2003 and *S48185A01226* Pearson LCCI Level 2 Certificate in Business Statistics

19 (c) Using the chart: (i) identify the general pattern in visitor numbers (ii) describe one exception to the pattern described in (c) (i). *S48185A01326* Pearson LCCI Level 2 Certificate in Business Statistics 13 15

20 As part of its business, the Capital Tourist Company provides guides to show visitors around London attractions. These tour guides are self-employed and are available only on days that are suitable for them. The Capital Tourist Company wants to know if availability is related to the years of service guides have with the company. Eight tour guides are selected and for each of them the length of service (in years) and the number of days available last year are recorded. The details are summarised in the table below. Guide A B C D E F G H Length of service (years) (x) Days available last year (y) (d) Explain why the response variable is days available last year. (e) (i) Plot the data on a scatter diagram, on the graph paper provided. (3) *S48185A01426* Pearson LCCI Level 2 Certificate in Business Statistics

21 (ii) Explain, in context, what the scatter diagram shows. *S48185A01526* Pearson LCCI Level 2 Certificate in Business Statistics 15 17

22 The data shown in the table is entered into a computer spreadsheet and the following results are produced: x = 64 y = 400 xy = 3805 x 2 = 618 (f) Calculate the equation of the least squares regression line for days available last year, given length of service (years). (6) (g) Interpret the value for the slope of the least squares regression line, calculated in (f). *S48185A01626* Pearson LCCI Level 2 Certificate in Business Statistics

23 (h) Estimate the number of available days for a tour guide with 11 years of service. (i) Give one reason why the least squares regression equation found in (f) should not be used to estimate the number of days available for a tour guide with 25 years of service. (Total for Question 3 = 20 marks) *S48185A01726* Pearson LCCI Level 2 Certificate in Business Statistics 17 19

24 4 The Sales Director of Saturn Engineering wishes to find the mean bonus payments (in ) made to sales employees. Before undertaking a larger study, the Sales Director takes a sample of eight sales employees and records their monthly bonus (a) For this sample, calculate the: (i) mean (ii) standard deviation. (3) A different engineering company, Jupiter Engineering, also gave bonuses in the same month to its own sales employees. The mean bonus, based on a sample of 12 sales employees was 60 and had a standard deviation of 8. (b) (i) Describe the differences in the distribution of bonuses paid by Saturn Engineering and Jupiter Engineering. *S48185A01826* Pearson LCCI Level 2 Certificate in Business Statistics

25 (ii) Calculate the coefficient of variation for Jupiter Engineering s sample of bonus payments. The Sales Director of Saturn Engineering adds data for a ninth sales employee to the original sample, causing the mean bonus to change to 50. (c) Calculate the value of this additional bonus payment. *S48185A01926* Pearson LCCI Level 2 Certificate in Business Statistics 19 21

26 Saturn Engineering has a team of eight salespeople who contact a number of internet retail sites each month. The value of sales generated ( 000), together with the number of internet retail sites contacted by each person during August 2015, is given in the following table. Salesperson Number of internet retail sites contacted Sales generated ( 000) A B C D E F G H (d) (i) Calculate the value of Spearman s rank correlation coefficient between number of internet retail sites contacted and sales generated. (7) *S48185A02026* Pearson LCCI Level 2 Certificate in Business Statistics

27 (ii) Interpret, in context, the value of the Spearman s rank correlation coefficient. The salespeople also visit the offices of prospective clients. The equivalent Spearman s rank correlation coefficient between sales generated and distances travelled by each salesperson during the same month was calculated using a statistical software package to be 0.62 (e) Compare this value with the value calculated in (d) (i), stating whether sites contacted or distance travelled is more reliable at indicating the value of sales. (Total for Question 4 = 20 marks) *S48185A02126* Pearson LCCI Level 2 Certificate in Business Statistics 21 23

28 5 A company involved with corporate mediation services carries out research into industrial disputes within the United Kingdom. The following table shows the number of work stoppages in the United Kingdom due to industrial disputes for the years 2011 to Year Number of work stoppages Jan Mar Apr Jun Jul Sep Oct Dec (Source: Crown copyright 2014) (a) Plot the data on a time-series graph, on the graph paper provided. (4) *S48185A02226* Pearson LCCI Level 2 Certificate in Business Statistics

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30 (b) Calculate the trend values for the data using a four-point centred moving average. (6) (c) Explain why any forecasts of future values are likely to be inaccurate, using your answers from (a) and (b). *S48185A02426* Pearson LCCI Level 2 Certificate in Business Statistics

31 One of the companies that had an industrial dispute over its wage demands was investigated further. The following data was collected from the company. Type of work Number of employees Weekly wage ( ) Number of employees Weekly wage ( ) Production Administration Estates Management (d) Calculate a base weighted index to show the increase in wages between 2010 and (6) *S48185A02526* Pearson LCCI Level 2 Certificate in Business Statistics 25 27

32 The estates staff had a wage increase of 10% between 2010 and (e) Explain why the base weighted index calculated in (d) gives a smaller wage increase than that achieved by the estates staff. (Total for Question 5 = 20 marks) TOTAL FOR PAPER = 100 MARKS *S48185A02626* Pearson LCCI Level 2 Certificate in Business Statistics

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34 Abbreviations Method Mark This is used to reward candidates where there is evidence of the candidate having adopted the correct method for a calculation, but where the accuracy of the answer is not necessarily being awarded a mark. A1 Accuracy Mark This is used to reward candidates who have attained the answer to a specific calculation representing a method in the question. If stated in the mark scheme, the own figure rule can be used with the accuracy mark. of Own Figure rule Accuracy marks can be awarded where the candidates answer does not match the mark scheme, though is accurate based on their valid method. cao Correct Answer Only rule Accuracy marks will only be awarded if the candidates answer is correct, and in line with the mark scheme. oe Or Equivalent rule This rule is used when the value of an answer may be presented in a variety of ways, such as fractions (simplified/non-simplified/mixed), decimals, percentages. The candidates answer must be equivalent in value to the mark scheme answer. awrt Anything Which Rounds To rule This rule is used when the candidate supplies a figure which rounds to the value determined by the mark scheme. 30 Pearson LCCI Level 2 Certificate in Business Statistics

35 Question Answer (AO1) 1 Mark 1(a)(i) Award 1 mark for any valid definition, e.g. Primary data is: Data collected by yourself Data used for its original purpose Not acceptable: first source of data Question Answer (AO1) 1 Mark 1(a)(ii) Award 1 mark for any valid definition, e.g. Secondary data is: data that is collected by some other person or /found using another source Not used for its original purpose Question Answer (AO1) 2 / (AO3) 2 Mark 1(b) Award 1 mark (AO2) for any correct example within 2 each box. Award 1 mark (AO3) for any correct advantage within each box 2 Source Example Advantage Primary Questionnaires/ interviews/ measurement/obser vation Secondary government databases/ newspapers/ academic journals/ the internet reliability of data is known readily available/ relatively inexpensive (4) Pearson LCCI Level 2 Certificate in Business Statistics 31

36 Question Answer (AO2) 2 Mark 1(c)(i) 360 x 58.0/total 360 x 58.0/134.3 = 155 A1 Question Answer (AO2) 2 Mark 1(c)(ii) 360 x 1.5/total 360 x 1.5/134.3 =4 A1 Question Answer (AO2) 2 Mark 1(d) 100% x ( )/total 100% x 80.4/134.3 =59.9% (accept 60%) A1 Question Answer (AO2) 2 Mark 1(e)(i) Award 1 mark for multiplying the two correct probabilities (0.25 x 0.7) OR Award 1 mark for multiplying one correct probability. Prob (company and not late) = 0.25 x 0.7 Prob (company) x Prob (late) = 0.25 x 0.7 Award full marks for correct answer only =0.175 A1 32 Pearson LCCI Level 2 Certificate in Business Statistics

37 Question Answer (AO3) 3 Mark 1(e)(ii) Award 1 mark for adding the two correct probabilities. Award 1 mark for both sides correct or 1 side correct. Prob (late) = Prob (owner and late) + Prob (company and late) = 0.75 x x 0.3 Award full marks for correct answer only =0.225 A1 (3) Question Answer (AO2) 3 Mark 1(f) Award 1 mark for subtracting candidate s answer in e(ii) from 1. Award 1 mark for squaring ( /of) Prob (on time) = = Prob (both on time) = x Award full marks for correct answer only = A1 (of) (3) Pearson LCCI Level 2 Certificate in Business Statistics 33

38 Question Answer (AO2) 4 / (AO3) 1 Mark 2(a) Cumulative frequencies 8, 20, 45, 85, 108, 120 Award 1(AO2) mark for calculating the cumulative frequencies by adding cumulatively Award 1 mark (AO3) for: A1 Linear scale Correct labelling of horizontal axis: cost Correct labelling of vertical axis: frequency Title not required Award 1 mark (AO2) for correct horizontal position of points Award 1 mark (AO2) for correct vertical position of points Award 1 mark (AO2) for increasing curve A1 A1 Increasing Curve A1(of) (5) 34 Pearson LCCI Level 2 Certificate in Business Statistics

39 Question Answer (AO2) 2 Mark 2(b)(i) Award 2 marks for correct answer only OR 2 marks for correct method and own figure rule. Award 1 mark for correct horizontal line at 60 but incorrect value identified. Median (from graph) cumulative frequency line at 60 = 310 (accept+/- 10) A1(of) Question Answer (AO2) 4 Mark 2(b)(ii) Q1 = 190(cumulative frequency line at 30, accept of) Q3 = 440 (cumulative frequency line at 90, accept of) QD = ( )/2 (accept of) = 125 (accept+/-10, or of) A1(of) (4) Question Answer (AO2) 2 Mark 2(b)(iii) Number below 500 is 100 % greater than 500 = 20/120 x 100 (accept of) = 17% (accept +/-2%, or of) A1 (of) Question Answer (AO3) 2 Mark 2(c) Award 1 mark for identifying a feature of the median that makes it a suitable measure. Award 1 mark for relating feature to the data. Median is not affected by extreme values because There are a small number of very high costs Pearson LCCI Level 2 Certificate in Business Statistics 35

40 Question Answer (AO3) 1 Mark 2(d) Award 1 mark for the correct method 1 systematic sampling Not acceptable: random sampling Question Answer (AO3) 1 Mark 2(e) Award 1 mark for applying sampling fraction 1 correctly, e.g.: every 12 th /or 1 in 12 / 1/12 Not acceptable: 12 Question Answer (AO3) 1 Mark 2(f) Award 1 mark for any valid response, e.g. 1 There may be bias if the population is listed in certain ways (e.g. male/female alternately) Question Answer (AO1) 2 Mark 2(g) Award 1 mark for each valid response up to a maximum of 2 marks (AO1), e.g. Higher response rate compared to paper/electronic methods of collection. More complex questions can be asked as the interviewer can probe/explain clearly Pearson LCCI Level 2 Certificate in Business Statistics

41 Question Answer (AO1) 1 Mark 3(a) Award 1 mark for correct type of chart, e.g. 1 Multiple bar chart/graph Comparative bar chart/graph Not acceptable: bar chart/graph only Question Answer (AO3) 1 Mark 3(b) Award 1 mark for correct answer only. 1 France Question Answer (AO3) 1 Mark 3(c)(i) Award 1 mark for correct description of general 1 pattern. Visitor numbers have increased (over this time) Not acceptable: visitor numbers have increased and decreased Question Answer (AO3) 1 Mark 3(c)(ii) Award 1 mark for any correct description, e.g. 1 There is a clear reduction in numbers from the USA There is no change in travel from the Irish Republic Question Answer (AO3) 1 Mark 3(d) Award 1 mark for correct explanation of why the 1 response variable is days available last year. The study investigates if availability is dependent on years of service (so availability is the dependent (or response) variable Not acceptable: because it is y Pearson LCCI Level 2 Certificate in Business Statistics 37

42 Question Answer (AO2) 2 / (AO3) 1 Mark 3(e)(i) Award 1 mark (AO3) for: A1 Linear scale Correct labelling of horizontal axis: years Correct labelling of vertical axis: days Title not required Award 2 marks (AO2) for all points correct. Award 1 (AO2) mark for 1 or 2 point errors 2 (3) 38 Pearson LCCI Level 2 Certificate in Business Statistics

43 Question Answer (AO3) 1 Mark 3(e)(ii) Award 1 mark for correct explanation of scatter diagram, e.g. 1 Guides with longer length of service tend to be more available. Not acceptable: positive correlation Question Answer (AO2) 6 Mark 3(f) n=8 A1 b n n xy x x 2 2 x y = 2 y a b n n x = A1 = = y = x (also accept y = x) A1 A1 (6) Question Answer (AO4) 2 Mark 3(g) Award 1 mark for correct interpretation and 1 mark stating the amount of increase in availability for each additional year of service. The slope (b) is positive so days available increases with length of service by about 5 to 6 extra days per additional year of service Pearson LCCI Level 2 Certificate in Business Statistics 39

44 Question Answer (AO2) 2 Mark 3(h) When x=11 y= x =67 days A1(of) Question Answer (AO3) 1 Mark 3(i) Award 1 mark for any valid reason, e.g. 1 Value of x is out of range of given data (extrapolation) No evidence that given relationship exists when x=25 (Do not accept interpolation ) 40 Pearson LCCI Level 2 Certificate in Business Statistics

45 Question Answer (AO2) 1 Mark 4(a)(i) Mean = x/n = 416/8 = 52 A1 Question Answer (AO2) 3 Mark 4(a)(ii) x 2 = Standard deviation = {23 396/ } = {220.5} = A1 A1(of) (3) Question Answer (AO3) 2 Mark 4(b)(i) Award 1 mark for description of the differences in distribution of bonus payments up to a maximum of 2 marks (AO3). Jupiter Engineering pays higher bonuses They are less spread out (more consistent amongst the sales employees) Question Answer (AO2) 2 Mark 4(b)(ii) Coefficient of variation = 8/ x 8/60 = 13.3% A1 Not acceptable: Pearson LCCI Level 2 Certificate in Business Statistics 41

46 Question Answer (AO2) 2 Mark 4(c) Total of 9 values is 9x50 = 450 Missing additional bonus payment = = 34 A1 Question Answer (AO2) 7 Mark 4(d)(i) Award 1 mark (AO2) for ranking sales and sites in order. Award 1 mark (AO2) for correct order of sales and sites. Award 1 mark (AO2) for correct tied ranks, both 3.5. A1 A1 Rankings A B C D E F G H Sites Sales d d 2 = 11.5 r sp = 1 (6x11.5)/(8x63) = A1(of) A1(of) (7) Question Answer (AO4) 1 Mark 4(d)(ii) Award 1 mark for correct interpretation of Spearman s rank correlation coefficient. An increase in internet sites contacted leads to an increase in sales. Not acceptable: strong positive correlation 42 Pearson LCCI Level 2 Certificate in Business Statistics

47 Question Answer (AO4) 2 Mark 4(e) Award 1 mark for stating the correlation between 1 distance travelled /sites contacted, e.g. Distance travelled/0.62 gives a lower correlation than sites contacted/0.86 Sites contacted/0.86 gives a higher correlation than distance travelled/0.62 Award 1 mark for correct interpretation of correlation. 1 Sites contacted is a better indicator of sales performance Travel distance is a poorer indicator of sales performance Pearson LCCI Level 2 Certificate in Business Statistics 43

48 Question Answer (AO2) 3 / (AO3) 1 Mark 5(a) Award 1 mark (AO3) for: A1 Linear scale Correct labelling of horizontal axis: years and quarters Correct labelling of vertical axis: frequency Title not required Award 2 marks (AO2) for all points correct. Award 1 mark (AO2) for 1 or 2 point errors Award 1mark (AO2) for joining points with straight lines. 2 1 (4) 44 Pearson LCCI Level 2 Certificate in Business Statistics

49 Question Answer (AO2) 6 Mark 5(b) Quarter Data Trend Q1 42 Q Q Q Q Q Q Q Q Q Q3 48 Q4 30 Add 4s A1 Add 2s A1(of) Trend A1(of) (6) Question Answer (AO3) 2 Mark 5(c) Award 1 mark for correct explanation of why forecasts of future values are likely to be inaccurate, up to a maximum of 2 marks. From moving averages - trend cannot be reliably determined / slight downward trend From graph - seasonal variations not clear / seasonal variations irregular Pearson LCCI Level 2 Certificate in Business Statistics 45

50 Question Answer (AO2) 6 Mark 5(d) p0q0 = 510 x x x x 25 = A1 p1q0 = 534x x x x 25 = Base weighted Index =100 x / = A1 A1(of) (6) Question Answer (AO3) 2 Mark 5(e) Award 1 mark for explanation of why the base 1 weighted index gives a smaller wage rise, e.g. Difference due to: small weight given by estates staff in the overall index / fewer estate staff Award 1 mark for second explanation point. smaller wage rises for other types of work 1 46 Pearson LCCI Level 2 Certificate in Business Statistics

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