0-13 Representing Data

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1 1. SURVEYS Alana surveyed several students to find the number of hours of sleep they typically get each night. The results are shown in the table. Make a bar graph of the data. Draw a histogram to represent the number of hours of sleep by student. The vertical scale is the number of hours of sleep play. The horizontal scale is the student. There is should be space between the bars. esolutions Manual - Powered by Cognero Page 1

2 2. PLAYS The frequency table shows the ages of people attending a high school play. a. Make a histogram to display the data. b. Make a cumulative frequency histogram showing the number of people attending who were less than 20, 40, 60, or 80 years old. a. Draw a histogram to represent the ages attending the play. The vertical scale is the number of people attending the play. The horizontal scale is the age range. There is no space between the bars. b. Draw a cumulative frequency histogram with the vertical axis representing the number of people and the horizontal axis representing the number of people below the age groupings given. esolutions Manual - Powered by Cognero Page 2

3 3. LAWN CARE Marcus started a lawn care service. The chart shows how much money he made over the first 8 weeks of summer break. Make a line graph of the data. Draw a line graph to represent the profit made each week. The vertical scale is the profit in dollars. The horizontal scale is weeks. Plot the points to represent the data. Draw a line connecting each pair of consecutive points. esolutions Manual - Powered by Cognero Page 3

4 Use each set of data to make a stem-and-leaf plot and a box-and-whisker plot. Describe how the outliers affect the quartile points. 4. {65, 63, 69, 71, 73, 59, 60, 70, 72, 66, 71, 58} The greatest place value is tens. So, the stems should be 5, 6, and 7. The leaves should be the values in the ones place. The data in order from least to greatest are 58, 59, 60, 63, 65, 66, 69, 70, 71, 71, 72, 73. Find Q 2 or the median first. Since there is an even number of values, find the mean of the middle two. Q 2 : The Q 1 is the median of the lower half of the data set. The lower half is {58, 59, 60, 63, 65, 66}. Since there is an even number of values, find the mean of the middle two. Q 1 : The Q 3 is the median of the upper half of the data set. The upper half is {69, 70, 71, 71, 72, 73}. Since there is an even number of values, find the mean of the middle two. Q 3 : There are no outliers. esolutions Manual - Powered by Cognero Page 4

5 5. {31, 30, 28, 26, 22, 34, 26, 31, 47, 32, 18, 33, 26, 23, 18} The greatest place value is tens. So, the stems should be 1, 2, 3, and 4. The leaves should be the values in the ones place. The data from least to greatest are 18, 18, 21, 23, 26, 26, 26, 28, 30, 31, 31, 32, 33, 34, 47. The median Q 2, or the middle number, is 28. The Q 1 is the median of the lower half of the data set. The lower half is {18, 18, 21, 23, 26, 26, 26}. The median of this half is 23. So, Q 1= 23. The Q 3 is the median of the upper half of the data set. The upper half is {30, 31, 31, 32, 33, 34, 47}. The median of this half is 32. So, Q 3= 32 The only outlier is 47. esolutions Manual - Powered by Cognero Page 5

6 6. FINANCIAL LITERACY The table shows how Ping spent his allowance of $40. Make a circle graph of the data. How Spent savings music snacks T-shirts Ratio Degrees for Section of Graph esolutions Manual - Powered by Cognero Page 6

7 7. JOGGING The table shows the number of miles Hannah jogged each day for 10 days. Make a line graph of the data. Draw a line graph to represent the number of miles jogged each day. The vertical scale is the number of miles. The horizontal scale is days. Plot the points to represent the data. Draw a line connecting each pair of consecutive points. 8. BASKETBALL Two basketball teams are analyzing the number of points they scored in each game this season. Lions: 48, 52, 55, 49, 53, 55, 51, 50, 46, 53, 47, 55, 50, 51, 60, 52, 57, 56, 58, 55 Eagles: 35, 39, 37, 40, 44, 42, 53, 42, 40, 44, 48, 46, 43, 47, 45, 41, 45, 43, 47, 48 a. Make a double box-and-whisker plot to display the data. b. How does the number of points scored by the Lions compare to the number of points scored by the Eagles? c. In the first game of the post season, a sports announcer reported the Lions scored a whopping 60 points. Is it appropriate for the announcer to use the word whopping in the statement? Is 60 an unusually high number of points for the Lions to score? Explain your answer. a. Enter the Lions values into L1 on a graphing calculator. Enter the Eagles values into L2. Turn the Stat Plot 1 on and specify box-and-whiskers plot with L1. Turn the Stat Plot 2 on and specify box-and-whiskers plot with L2. To graph, ZoomStat first. esolutions Manual - Powered by Cognero Page 7

8 b. Calculate the quartiles. Lions Eagles For Lions Q 3 Q 1 is 55 5 or 5. For the Eagles. Q 3 Q 1 is or 6. Thus, the interquartile range for both teams is about the same. esolutions Manual - Powered by Cognero Page 8

9 If you compare the medians Lions is 52.5 compared to 43.5 for the Eagles. If you compare the means, Lions is 52.7 compared to 73.5 for the Eagles. Therefore, all quartiles of the Lions scores are shifted to the right of those of the Eagles, meaning the Lions have a higher average score. c. No, 60 is not an unusually high score for the Lions. It is higher than the average, but not by much. 9. TESTS Mr. O Neil teaches two algebra classes. The test scores for the two classes are shown. a. Make a double box-and-whisker plot to display the data. b. Write a brief description of each data distribution. c. How do the scores from the third period class compare to the scores from the sixth period class? a. Enter the 3rd periods values into L1 on a graphing calculator. Enter the Sixth periods values into L2. Turn the Stat Plot 1 on and specify box-and-whiskers plot with L1. Turn the Stat Plot 2 on and specify box-and-whiskers plot with L2. To graph, ZoomStat first. [63.8, 102.2] scl:1 b. Calculate the quartiles using a graphing calculator. From the CALC option on the STAT menu, select 1-Var Stats. Use 2nd L1 or 2nd L2 to specify the class period. 3rd period esolutions Manual - Powered by Cognero Page 9

10 3rd period 6th period For 3rd period Q 3 Q 1 is or 8.5. For the 6th period. Q 3 Q 1 is or 11. Thus, the interquartile range for 6th period is larger than 3rd period. For 3rd period, the minimum score is 67 and highest 99. For 6th period, the minimum score is 70 and maximum is 95. The median for 3rd period is 84.5 compared to 88 for 6th period. Most of the data for third period are spread fairly evenly from about 80 to 89, with the lowest score being 67 and the highest score being 99. Most of the data for sixth period are between 79 and 91, with the lowest score for the class being 70 and the highest score being 95. c. The sixth period class has a smaller range, a higher median, and a larger interquartile range than the third period class. esolutions Manual - Powered by Cognero Page 10

11 Which type of graph is the best way to display each set of data? Explain. 10. an organization s dollar contributions to 4 different charities Since four charities represent category data and contribution amounts are numeric, a bar graph is the best way to display the data. 11. the prices of a college football ticket from 1990 to the present Since, the data would show change over time, a line graph would give a clear picture of the change in the cost of a seat changes over time. 12. the percent of glass, plastic, paper, steel, and aluminum in a recycling center Since, the data will show how parts are related to a whole, a circle graph would provide a clear distribution of the different products recycled at the recycling center. 13. DISCUS The winning distances for the girls discus throw at an annual track meet are shown below. a. Make a stem-and-leaf plot to display the winning distances. b. Make a histogram to display the winning distances. c. What does the stem-and-leaf plot show you that the histogram does not? d. If this trend continues, what would you expect the winning distance to be in 2030? Is your answer reasonable? Explain. a. Look at the data to find the least place value. The least place value is the ones. Let the leaves in the stem-and-leaf plot be the digits in the ones place. So, 119 m would have a stem of 11 and a leaf of 9. b. The distances in the table range from 119 to 140. Use 10-unit intervals on the frequency table. Distance Frequency esolutions Manual - Powered by Cognero Page 11

12 Draw and label a horizontal and vertical axis. Include a title. Show the intervals from the frequency table on the horizontal axis. For each height interval, draw a bar whose height is given by the frequencies. There is no space between the bars. c. The histogram shows the frequencies of groups of data while the stem-and-leaf plot shows every data value. Notice in this case that the stems are equivalent to the size of the intervals and the number of leaves for each stem is equal to the corresponding frequency. d. From looking at the table, the winning distance increased by 16 meters from 2000 to This could be seen easier with a line graph. If the distance increases by 16 meters every 10 years, in 2030 the winning distance will be 32 meters more than in 2010, or 172 meters. It is unreasonable to expect that every year girls will be able to throw farther and farther, at esolutions Manual - Powered by Cognero Page 12

13 some time the distance will level off. 14. DRINKS Tate is buying drinks for a party. He is comparing 2-liter bottles to 12-packs of 12-ounce cans. The prices of 2-liter bottles are $0.99, $1.99, $1.87, $1.79, $1.29, $1.43, and $1.15. The prices of 12-packs are $2.50, $4.25, $3.34, $2.65, $3.19, $3.89, and a. Make a double box-and-whisker plot to display the data. b. Notice that instead of comparing price per item it would be more beneficial to compare price per ounce. What is the price per ounce of each item if a 2-liter is approximately 67 ounces and a 12-pack is 144 ounces? Round to the nearest cent. c. Make a new double box-and-whisker plot from the data obtained in part b. d. Which is the better deal, the 12-packs of cans or the 2-liter bottles? Explain. a. To create a box-and-whiskers with out technology, determine the quartiles, interquartile range and identify any outliers. 2-liter bottles: Order the data from least to greatest and determine the quartiles. 0.99, 1.15, 1.29, 1.43, 1.79, 1.87, 1.99 Q 1 = 1.15, Q 2 = 1.43, and Q 3 = 1.87 Determine the interquartile range. IQR = Q 3 Q 1 = = 0.72 Check to see if there are any outliers (0.72) = (0.72) = 2.93 Prices less than 0.07 or greater than 2.93 are outliers. Therefore, there are no outliers. 12-packs: Order the data from least to greatest and determine the quartiles. 2.50, 2.65, 2.99, 3.19, 3.34, 3.89, 4.25 Q 1 = 2.65, Q 2 = 3.19, and Q 3 = 3.89 Determine the interquartile range. IQR = Q 3 Q 1 = = 1.24 Check to see if there are any outliers (1.24) = (1.24) = 5.75 esolutions Manual - Powered by Cognero Page 13

14 Prices less than 0.79 or greater than 5.75 are outliers. Therefore, there are no outliers. Draw the plots using the same number line. Draw a number line that includes the least and greatest numbers in the data. Place dots above the number line to represent the quartiles and the ends of the whiskers. Draw the boxes and whiskers. The vertical lines go through the quartiles. To use graphing technology for the box-and-whiskers plots, enter the 2-litter values into L1 on a graphing calculator and the 12-pack values into L2. Turn the Stat Plot 1 on and specify box-and-whiskers plot with L1. Turn the Stat Plot 2 on and specify box-and-whiskers plot with L2. To graph, ZoomStat first. b. Divide the 2-liters values by 67 and the 12-pack values by 144. If the data is already entered into a graphing calculator as L1 and L2, then set L3 to equal and L4 equal to. 2-liters: $0.01, $0.03, $0.03, $0.03, $0.02, $0.02, $ packs: $0.02, $0.03, $0.02, $0.02, $0.02, $0.03, $0.02 c. For the 2-liter data Q 1 = 0.02, Q 2 = 0.02, and Q 3 = For the 12-pack data Q 1 = 0.02, Q 2 = 0.02, and Q 3 = d. There is not a significant difference in price per ounce. The 2-liters are between $0.01 and $0.03 per ounce and the 12-packs are between $0.02 and $0.03 per ounce. esolutions Manual - Powered by Cognero Page 14

Practice Test Unit 06B 11A: Probability, Permutations and Combinations. Practice Test Unit 11B: Data Analysis

Practice Test Unit 06B 11A: Probability, Permutations and Combinations. Practice Test Unit 11B: Data Analysis Note to CCSD HS Pre-Algebra Teachers: 3 rd quarter benchmarks begin with the last 2 sections of Chapter 6 (probability, which we will refer to as 6B), and then address Chapter 11 benchmarks (which will