FINALS REVIEW BELL RINGER Simplify the following expressions without using your calculator. 1) 6 2/3 + 1/2 2) 2 * 3(1/2 3/5) 3) 5/3 + 7 + 1/2 4 4) 3 + 4 ( 7) + 3 + 4 ( 2) 1) 36/6 4/6 + 3/6 32/6 + 3/6 35/6 2) 2 * 3(5/10 6/10) 2 * 3( 1/10) 2 * 3/10 6/10 3/5 3) 10/6 + 42/6 + 3/6 24/6 55/6 24/6 31/6 4) 3 4 + 7 3 4 + 2 1 + 7 3 4 + 2 6 3 4 + 2 3 4 + 2 1 + 2 1 After finishing the bell ringer, pull out the histogram (NBA points scored) you made last class. Please then input the data into the calculator and make the histogram on your calculator. 1
Homework Answers 2a) 14.5% 2b) $1,317,000 2c) $21,242 2d) The mean will increase and the median and mode will stay the same. 2e) $1,404,000 3a) observations will differ 3b) Cyprus consumed the least. 3c) The per capita consumption is 243.52 million Btu's 3d) US is approximately 272.7 million and Cuba is 11.2 million 3e) The data is skewed to the right with one peak and an outlier between 90 and 100 million. 3f) No, it does not make sense to find an average energy consumption because each country varies greatly in population. 3g) The U.S. is the farthest to the right. It is no where close the the other countries because we consume more energy and are much wealthier than the other countries on the list. 2
Homework Answers 4a) Observations may vary. There are many countries that use between 100 and 200 million BTU per capita. Only six countries use more than 200 million and there are no outliers. The graph has one peak and a gap between 300 350 million. 4b) This histogram is not as strongly skewed and does not have any outliers 4c) The median is around 170. That means half of the countries consume more the 170 million BTU's per person and half the countries consume less. 4d) Greatest Consumption U.S., Japan, Germany, Canada, France Greatest Per Capita Consumption Norway, Canada, U.S., Australia, Netherlands 5a) The estimated mean and median are both around 22. The median says that half the countries have more than 22% of their population aged 5 14 years and half less. The mean says the most countries have 22% of the population aged 5 14. 5b) The estimated mean is 2,300 while the median is around 1,400. This median says that half the states receive over $1,400 million per year in combined sales and half less. The mean says that the average state sells $2,300 million per year 5c) The estimated mean is 120 and the median is 100. 3
BOX PLOTS AND PERCENTILES Percentile is a special relationship that tells us what percentage of things are equal or less than what we want. Ex1: You scored in the 83rd percentile on the MAP testing. This means that 83% of the students who took the test scored the same as you or less. What is a Percentile? (hint: What is a percent?) Ex2: You are 64 inches tall and 11 years old. You are in the 97th percentile for your height in the united states. This means that 97% of 11 year olds in this country are your height or shorter. A percentile is a way to use percentages to understand the relationship of LARGE POPULATIONS. So How do we calculate a percentile? Simple, find the percentage! Here is how percenle is computed. Look at this list of 13 scores: 48, 52, 58, 64, 70, 74, 79, 84, 89, 93, 96, 97, 100. Let's look at the score 93. 10 scores were equal to, or lower than 93. To compute your percenle, we just do 10 / 13, to get.77 (rounded). To covert to a percent, just move the decimal two places to the right, to get 77%. We say that the score 93 is in the 77th percenle. That means that 93 is equal to or beer than 77% of the other scores. Question: Is this list of 13 scores a Large Population? Is this statistic meaningful? 4
BOX PLOTS AND PERCENTILES Box Plots are the distributions that depict Percentiles Just like percentages, percentile is based out of 100% however it is impossible to have 100% of a population be equal or less than everything else in the population. The highest percentile is 99% because a value cannot be less than itself. The lowest percentile is 0%. Box Plots use Quartiles (quarters) of the distribution. The three quartiles are 25%, 50%, 75%. Obviously the 50% is the middle number so it is computed with the Median of the entire distribution. Since 25% is the middle between 0 and 50, it can be found by taking the median of the lower half of the data. Therefore 25% is called the Lower Quartile. (LQ) Since 75% is the middle between 50 and 99* it can be found by taking the median of the upper half of the data. Therefore 75% is called the Upper Quartile. (UQ) We draw a box plot with the quartiles as vertical bars. 25% LQ 50% Median 75% UQ These numbers are on an imaginable number line that runs through the middle of the vertical lines. To help us see the data we connect the vertical lines to make a box 25% LQ 50% Median 75% UQ To finish we plot the lowest (min) and highest (max) value from the distribution on the out side of the box on the number line. Lowest Value (min) Highest Value (max) 25% LQ 50% Median 75% UQ ** Please notice that these values are on a invisible number line so there should be consistency in the spacing between the lines that represent the min, max, LQ, median, UQ 5
Lastly, the benefit of the Box Plot is that we can easily see Outliers and Skewness. You need to know that the length of the box is important and it is called the Interquartile Range (IQR). Range = Max Min Interquartile Range = Upper quartile Lower quartile (IQR = UQ LQ) Let's look at some stats about Lindblom and see how Percentile is used in the real world. Lindblom Stats 6
Height and Weight Percentiles http://pediatrics.about.com/cs/usefultools/l/bl_kids_centils.htm 7
Let's Practice making Box Plots. Look at the following data sets. You have the next 10 minutes to create a box plot for each car. If you finish early try and make a box plot on the TI 84 Calculator. 8
Using the data below, create three box plots and answer the following questions. 9
HMWK POW #9 10
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