Algebra. Chapter 10: Data Analysis. Name: Teacher: Pd:

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1 Algebra Chapter 10: Data Analysis Name: Teacher: Pd:

2 Table of Contents o Chapter 10-2 (Day 1): SWBAT: Construct Histograms Pgs: #1 6 HW: Pgs 7-10 o Chapter 10-3 (Day 2): SWBAT: Calculate the Central Tendency of a Data Set. Pgs: #11 15 HW: Pgs o Chapter 10-3 (Day 3): SWBAT: Calculate the Central Tendency of a Grouped Data. Pgs: #19 22 HW: Pgs o Chapter 10-3 (Day 4): SWBAT: Calculate Percentiles Ranks and Create box-and-whisker plots. Pgs: #26 30 HW: Pgs o Half Period Quiz Lessons: 10-1 to 10-3 o Chapter A (Day 5): SWBAT: Distinguish between different types of data Pgs: #34-43 HW: Page 44 o Chapter A (Day 6): SWBAT: Create trend lines to make predictions. Pgs: #45-51 HW: Pgs o Full Period Quiz Lessons: 10-3 to A o Day 7 - REVIEW Pgs: #54-58 o Day 8 - REVIEW Pgs: #59-62 o TEST

3 Day 1 - Frequency Histograms Warm Up Construct a stem-and-leaf plot listing the scores below in order from lowest to highest. 15, 25, 28, 32, 39, 40, 43, 26, 50, 75, 65, 19, 55, 72, 50 The of a data value is the number of times it occurs. A shows the frequency of each data value. If the data is divided into intervals, the table shows the frequency of each interval. A is a bar graph used to display the frequency of data divided into equal intervals. The bars must be of equal width and should touch, but not overlap. 1

4 1) The Jacksonville High School Varsity Boys basketball team had an excellent season, compiling a record of 15 5 (15 wins and 5 losses). The total points scored by the team for each of the 20 games are listed below in the order in which the games were played: 76, 55, 76, 64, 46, 91, 65, 46, 45, 53, 56, 53, 57, 67, 62, 64, 67, 52, 58, 62 (a) Complete the frequency table below. POINTS SCORED TALLY FREQUENCY (b) On the graph grid provided, create a histogram using the frequency table from above. 2

5 Cumulative Frequency Histograms shows the frequency of all data values less than or equal to a given value. You could just count the number of values, but if the data set has many values, you might lose track. Recording the data in a cumulative frequency table can help you keep track of the data values as you count. Example 2: 3

6 Example 3: Twenty students were surveyed about the number of days they played outside in one week. The results of this survey are shown below. {6, 5, 4, 5, 0, 7, 1, 5, 4, 4, 3, 2, 2, 3, 2, 4, 3, 4, 0, 7} Complete the frequency table for these data Number of Days Outside Interval Tally Frequency Complete the cumulative frequency table using these data. Number of Days Outside Cumulative Interval Frequency What must the last entry of the cumulative frequency table always be equal to? Explain. Create a cumulative frequency histogram based on the table you made. 4

7 Example 4: The Cumulative Frequency Histogram below shows test scores from an Algebra Regents Exam. a) Determine the total number of students who took the Algebra Regents Exam. b) Determine how many students scored higher than 70. c) State which ten-point interval contains the median. d) State which ten-point interval doubled another ten-point interval. 5

8 SUMMARY Exit Ticket

9 Day 1 - HW Section 1: Histograms 2) 3) 7

10 4) 5) In which interval is the median? Which two intervals have the same percentages? 8

11 6) Jim Shorts is a star basketball player for the Arlington High School basketball team. The number of points scored by Jim in each of his last 20 games are as follows: 35, 28, 25, 34, 41, 26, 19, 23, 32, 20, 11, 8, 38, 48, 22, 25, 16, 19, 22, 40 (a) Complete the table below to find the number in each interval. Construct a frequency histogram. Interval Tally Frequency 0 to 9 10 to to to to 49 (b) Complete the table below to determine the cumulative frequency. Construct a cumulative frequency histogram. Interval 0 to 9 0 to 19 0 to 29 0 to 39 0 to 49 Cumulative Frequency 9

12 7) The scores on a mathematics test were 70, 55, 61, 80, 85, 72, 65, 40, 74, 68, and 84. Complete the accompanying table, and use the table to construct a frequency histogram for these scores. Score Tally Frequency Complete the table below to determine the cumulative frequency. Construct a cumulative frequency histogram Score Cumulative Frequency 10

13 Chapter 10 2 (Day 2) Warm Up MEAN: the average Steps: 1. add up all the numbers of a set 2. divide the sum by the total number of numbers MEDIAN: middle value when the values are in numerical order or the mean of the two middle values if there is an even number of values MODE: the value or values that occur most often. There may be one mode or more than one mode. If no value occurs more often than another, we say the set has no mode. A measure of central tendency describes how data clusters around a value. 11

14 1) Lucia took five tests in her English class. The first four test scores are: 88, 85, 90, 94 If she has an average of a 90, what is her 5 th test score? 2) A student had taken six tests and received scores of 88, 73, 81, 83, 79, 94. The seventh test was coming up and the student want to know what was needed on the seventh test to have a mean score of 83. Find the seventh test score. Consider this set of test score values: Normal listing of scores. Scores with the lowest score replaced with outlier. The two sets of scores above are identical except for the first score. The set on the left shows the actual scores. The set on the right shows what would happen if one of the scores was WAY out of range in regard to the other scores. Such a term is called an outlier. With the outlier, the mean changed. With the outlier, the median did NOT change. 3) In Mr. Smith s Advanced Calculus Course, eight students recently took a test. Their grades were as follows: 45, 78, 82, 85, 87, 89, 93, 95 (a) Calculate the mean and median of this data set. (b) What score is an outlier in this data set? (c) Which value, the mean or the median, is a better measure of how well the average student did on Mr. Smith s quiz? 12

15 4) The data below shows the prices of jeans at different department stores around the city. (a) Calculate the mean, median, and mode for this data set. Round to the nearest tenth if necessary. Mean: Median: Mode: (b) Are there any outliers in this data set? If so, what data value? (c) What effect does this outlier have on the mean value? (d) Which statistical measure best represents the prices of jeans at different department stores around the city? 13

16 In Conclusion: If a number c is added to each set of data, then. New mean = New Median = New Mode = It can also be shown to have a similar result holds for multiplicative transformations, that is If a number c is multiplied to each set of data, then. New mean = New Median = New Mode = Example 5: 14

17 Challenge SUMMARY Exit Ticket 15

18 Day 2 - HW

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21 Chapter 10 2 (Day 3) SWBAT: Calculate the measure of Central Tendencies when the data is grouped. Warm Up Mean: Median: Mode: 19

22 For this set of data, find: a. The total frequency b. The interval that contains the median c. The modal interval 20

23 Practice Problems 1) A survey was conducted to determine the average income of residents of a particular neighborhood. Twenty people were surveyed outside of a grocery store. The results of this survey are given in the table below. (a) Calculate the mean, median and mode income based on this survey. List the data below in numerical order. Mean: Median: Mode: (b) Are there any outliers in this data set? If so, what data value? (c) What effect does this outlier have on the mean value? 2) For this set of data, find: a. The total frequency b. The interval that contains the median c. The modal interval Challenge 21

24 SUMMARY Exit Ticket ANSWER Exit Ticket

25 Day 3 HW 23

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28 Percentiles and Box and Whisker Plots Day 4 SWBAT: Calculate Percentiles Ranks and Box and Whisker Plots Warm- Up Example #1: Computing Percentile Rank A percentile rank is the percentage of scores that fall at or below a given score. Percentile ranks are an easy way to convey an individual's standing at graduation relative to other graduates. Example 1: The data below represents the heights of 20 students. 53, 60, 61, 63, 64, 65, 65, 65, 65, 66, 66, 67, 67, 68, 69, 70, 70, 71, 71, 73 a) Find the percentile rank of , 60, 61, 63, 64, 65, 65, 65, 65, 66, 66, 67, 67, 68, 69, 70, 70, 71, 71, 73 b) Find the percentile rank of , 60, 61, 63, 64, 65, 65, 65, 65, 66, 66, 67, 67, 68, 69, 70, 70, 71, 71, 73 26

29 c) Example #2: Computing Percentiles (Quartiles) A percentile is a measure that tells us what percent of the total items in a data set is at of below that measure. Understanding Percentiles On a quiz taken by 30 students, a score of 85 is the 60 th percentile. A. How many students scored 85 or lower? B. How many students scored higher than 85? Quartiles can be thought of as percentile measure. Remember that quartiles break the data set into 4 equal parts. If 100% is broken into four equal parts, we have subdivisions at 25%, 50%, and 75% creating the: First quartile (lower quartile) to be at the 25 th percentile. Median (or second quartile) to be at the 50 th percentile. Third quartile (upper quartile) to be a the 75 th percentile. Example 3: For the table below, find the intervals in which the first, second and third quartiles lie. 27

30 Practice: Computing Percentiles (Quartiles) 4. Box and Whisker Plot Minimum: the smallest value in the set 1 st Quartile: the middle value in the first half of the set 2 nd Quartile: the middle value 3 rd Quartile: the middle value in the second half of the set 5) The average length in inches of the ten longest bones in the human body are listed. Use a graphing calculator to make a box-and-whisker plot to display the data 58, 63, 40, 44, 57, 59, 61, 53, 54, 58, 57, 57, 58, 58, 56 Minimum: 1 st quartile: 2 nd quartile (median): 3 rd quartile: Maximum: 28

31 6) Shown below are the scores 16 students received on a math quiz. Label the Minimum, Q1, Q2, Q3, and Maximum. 52, 60, 66, 66, 68, 72, 72, 73, 74, 75, 80, 82, 84, 91, 92, 98 Minimum: 1 st quartile: 2 nd quartile (median): 3 rd quartile: Maximum: 7) 8) Average Monthly High Temperatures (a) What percent of the time is it above 35? Daily Number of Minutes Seniors Watch TV (a) What percent of seniors watch less than 60 minutes of TV a day? (b) What percent of the time is it below 80? (b) What percent of seniors watch 15 minutes or more of TV a day? 29

32 SUMMARY Exit Ticket According to the box-and-whisker plot shown below, what are the five statistical summary values? 30

33 Day 4 - Homework 1) The Final Exam test scores were: 62, 66, 71, 75, 75, 78, 81, 83, 84, 85, 85, 87, 89, 89, 91, 92, 93, 94, 95, 99. Find the percentile rank for a score of 85 on this test 2) The heights of students in inches in Block 3 math class are 55, 59, 59, 60, 61, 63, 64, 64, 65, 68, 68, 69, 72, 74. Find the percentile rank for a height of 61 inches. 3) 4) 31

34 5) Twenty of Mr. Greco s physics students recently took a quiz. The results of this quiz are shown in the following box-and-whiskers diagram. Assume that all scores are whole numbers (a) What is the median score of the math quizzes? (b) What is the range of the scores on the math quizzes? (c) Mr. Greco regularly sets the passing grade on his quizzes to be the score of the lower quartile. What is the passing grade on this quiz? (d) What is the highest score on Mr. Greco s quiz? 6) 7) 32

35 8) The number of itunes downloaded by 25 students in one week ranges from 15 to 55. The box-and-whisker plot below depicts this data. For this data: a.) What is the minimum number of itunes downloaded? b.) What is the maximum number of itunes downloaded? c.) What is the number of itunes at the 25th percentile? d.) What is the number of itunes at the 50th percentile? e.) What is the number of itunes at the 75th percentile? 33

36 Chapter A (Day 5) Characterizing Data SWBAT: Distinguish between different types of data Warm Up Example 1: Differentiating Between Qualitative Data and Quantitative Data Qualitative Data: is data that is descriptive but not numeric. For example, if you ask your classmates, how do you feel about studying algebra? you may get qualitative responses like interesting, difficult, and challenging. Quantitative Data: refers to data that is represented by counts or measurements. For example, a list showing the numbers of students taking Mathematics, English, and Social Studies is a quantitative data list. 34

37 Freshman Class Practice For questions 1 4, determine if the data listed is quantitative data or qualitative data. 35

38 Example 2: Differentiating Between Univariate Data and Bivariate Data Data may be used to represent one variable, such as h for the heights of NBA players. Data that represents one concept or variable is called univariate data. Univariate data is often displayed in a frequency table, a histogram, a stem-and-leaf plot, or a box-and-whisker plot. Data that shows a relationship between two quantities is called bivariate data and requires two variables. The number of students in a school (n) and the yearly budget for the school (b) is an example of bivariate data. The data sets are related because the budget for a small school will be less than the budget for a large school. 36

39 Practice For questions 5 9, determine if the problem deals with univariate or bivariate data. 37

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41 Example 3: Possibly Biased Data When viewing statistics, you should consider: Who collected the data? Does the group collecting the data have an interest in how the results turn out? Is the study a recent study, or did it occur decades ago? Could recent developments have changed the findings? What is the sample size of the study? How many people/items were studied? Is the data from a primary source? Or has the data been "condensed" by another group? Do the statistics show any bias? Example: A study on the hazards of cigarette smoking being done by a tobacco company. (may not be reliable findings - conflict of interest) Example: Decades past, second-hand cigarette smoke was found to not be hazardous. More recent findings prove that this is not true. (findings should be current) Example: A study is done on the favorite color of 14 year olds. The sample group for the study is Mrs. Smith's third period class containing 20 students. (too few participants to generalize a finding to all 14 year olds) Example: The US Census Bureau collects data on US populations. A tabloid magazine publishes a synopsis of the findings. (the most reliable information comes from the original source - avoid the "Reader's Digest" condensed version by another publisher who may be interpreting the findings) Example: The study of how many people can walk a balance beam is conducted with students from a gymnastics class. (the results are biased due to the very specific selection of the participants) For questions 10-13, determine if the situation is biased. 39

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43 Practice Tell whether each data set is qualitative or quantitative. 1. The number of persons per square mile in each state. 2. An inventory list at a used CD store describing each in-stock item as excellent condition, very good condition, good condition, or poor condition. 3. A restaurant survey rating its food presentation as unique, tasteful, or ordinary. 4. The ages of people who flew from San Francisco to New York City in December Shopping: A survey conducted at an outlet mall asked shoppers to rate the success of their visit as very successful, somewhat successful, or not successful. Tell whether each data set is univariate or bivariate. Then create an appropriate display to represent the data. 6. The ages of the first ten presidents of the United States at their inauguration: {57, 61, 57, 57, 58, 57, 61, 54, 68, 51} 7. The elevations above sea level of the Great Lakes: Erie, 569ft; Huron, 577ft; Michigan, 577ft; Ontario, 243ft; Superior, 600ft. 41

44 8. Meteorology: The heat index is a measure of how hot it feels outside when the humidity changes. The table below gives the heat index for different levels of humidity when the actual temperature is 90 F. Is this data univariate or bivariate? 9. A survey completed at a large university asked 2, 000 students to estimate the average number of hours they spend studying each week. Every tenth student entering the library was surveyed. The data showed that the mean number of hours that students spend studying was 15.7 per week. Which characteristic of the survey could create a bias in the results? 1) The size of the sample 2) The size of the population 3) The method of analyzing the data 4) The method of choosing the students who were surveyed 10. Which of these questions is a biased question? 1) Do you prefer yogurt or pudding for dessert? 2) Do you prefer to sit on the couch and watch TV or do you like to exercise and stay in shape? 3) What sport do you play? 4) What is your favorite food? 42

45 Summary Exit Ticket 43

46 Practice Problems Day 5 - Homework 1) Which situation describes a correlation that is not a causal relationship? (a) The rooster crows, and the Sun rises. (b) The more miles driven, the more gasoline needed. (c) The more powerful the microwave, the faster the food cooks. (d) The faster the pace of a runner, the quicker the runner finishes. 3) Which relationship can best be described as causal? (a) height and intelligence (b) shoe size and running speed (c) number of correct answers on a test and test score (d) number of students in a class and number of students with brown hair 5) Which data set describes a situation that could be classified as qualitative? (a) the ages of the students in Ms. Marshall s Spanish class (b) the test scores of the students in Ms. Fitzgerald s class (c) the favorite ice cream flavor of each of Mr. Hayden s students (d) the heights of the players on the East High School basketball team 7) Which method of collecting data would most likely result in an unbiased random sample? (a) selecting every third teenager leaving a movie theater to answer a survey about entertainment (b) placing a survey in a local newspaper to determine how people voted in the 2004 presidential election (c) selecting students by the last digit of their school ID number to participate in a survey about cafeteria food (d) surveying honor students taking Mathematics B to determine the average amount of time students in a school spend doing homework each night 2) Which situation should be analyzed using bivariate data? (a) Ms. Saleem keeps a list of the amount of time her daughter spends on her social studies homework. (b) Mr. Benjamin tries to see if his students shoe sizes are directly related to their heights. (c) Mr. DeStefan records his customers best video game scores during the summer. (d) Mr. Chan keeps track of his daughter s algebra grades for the quarter. 4) Which data set describes a situation that could be classified as qualitative? (a) the elevations of the five highest mountains in the world (b) the ages of presidents at the time of their inauguration (c) the opinions of students regarding school lunches (d) the shoe sizes of players on the basketball team 6) A school wants to add a coed soccer program. To determine student interest in the program, a survey will be taken. In order to get an unbiased sample, which group should the school survey? (a) every third student entering the building (b) every member of the varsity football team (c) every member in Ms. Zimmer s drama classes (d) every student having a second-period French class 8) A survey is being conducted to determine which types of television programs people watch. Which survey and location combination would likely contain the most bias? (a) surveying 10 people who work in a sporting goods store (b) surveying the first 25 people who enter a grocery store (c) randomly surveying 50 people during the day in a mall (d) randomly surveying 75 people during the day in a clothing store 44

47 Chapter A (Day 6)Trend Lines SWBAT: Create trend lines to make predictions. Warm Up Definition: A scatter plot is a graph with points plotted to show a possible relationship between two sets of data. Describing Correlations from a Scatter Plot Definition A correlation describes a relationship between two data sets. A graph may show the correlation between data. 45

48 Directions: Describe the correlation between the variables as positive, negative, or no correlation. Matching Scatter Plots to Situations 1) Choose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs. Explain. GRAPH A GRAPH B GRAPH C 46

49 2) Choose the scatter plot that best represents the relationship between the number of minutes since a pie has been taken out of the oven and the temperature of the pie. Explain. GRAPH A GRAPH B GRAPH C Graphing a Scatter Plot from Given Data 1) The table shows the percent of people ages who report they voted in the presidential elections. Graph a scatter plot using the given data. b) Describe the correlation: 47

50 2) The table shows the number of soft drinks sold as a small restaurant from 11:00 am to 1:00 pm. (a) Graph a scatter plot using the given data. (b) Describe the correlation: 3) The table shows the average salary (rounded to the nearest hundred) for one type of worker, listed by decade. (a) Graph a scatter plot using the given data. (b) Describe the correlation: (c) Draw a trend line and determine the equation. (d) Based on the trend line, what is your prediction for the average salary in

51 4) Neal kept track of the number of minutes it took him to assemble sandwiches at his restaurant. The information is in the table below. (a) Create a scatter plot using the table. (b) Describe the correlation: (c) Draw a trend line and determine the equation. (d) Based on the trend line, what is your prediction for the time it will take to assemble 14 sandwiches. 49

52 5) The average number of gallons of coffee per person consumed in the United States is shown in the table below. (a) Create a scatter plot using the table. (b) Describe the correlation: (c) Draw a trend line and determine the equation. (d) Based on the trend line, what is your prediction for the number of gallons of coffee consumed in

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54 Day 6 Scatter Plots HW 52

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56 Data and Statistics Review Day 7 Find the mean, median, mode, and range for the following sets of data listed below. 1) 13, 14, 15 2) 5, 6, 7, 7, 8, 9 Mean: Median: Mean: Median: Mode: Range: Mode: Range: 3) 20, 20, 20, 20 4) 15, 6, 2, 8, 5, 10, 16, 12 Mean: Median: Mean: Median: Mode: Range: Mode: Range: 5) Rosario and Enrique are in the same mathematics class. On the first five tests, Rosario received scores of 78, 77, 64, 86, and 70. Enrique received scores of 90, 61, 79, 73, and 87. How much higher was Enrique s average than Rosario s average? 6) From January 3 to January 7, Buffalo recorded the following daily high temperatures: 5, 7, 6, 5, and 7. Which statement about the temperatures is true? (a) 15 points (b) 2 points (c) 3 points (d) 4 points (a) mean = median (b) mean = mode (c) median = mode (d) mean median 54

57 The accompanying box-and-whisker plot represents the scores earned on a science test. 7) According to the diagram shown, what is the median score? (a) 75 (c) 85 (b) 70 (d) 77 8) According to the diagram shown, what score represents the first quartile? (a) 55 (c) 100 (b) 70 (d) 75 9) What statement is not true about the box and whisker plot shown? (a) 75 represents the mean score (b) 100 represents the maximum score (c) 85 represents the 3rd quartile (d) 55 represents the minimum score 10) A score of an 85 on the box-and-whisker plot shown refers to (a) the third quartile (b) the maximum score (c) the median (d) the mean The number of text messages 10 different students sent in 1 day is shown in the box-and-whisker plot below. 11) What is the minimum number of text messages sent according to the plot shown? (a) 0 (c) 2 (b) 20 (d) 8 12) What number is at the 50th percentile according to the plot shown? (a) 12 (c) 8 (b) 14 (d) 10 13) According to the plot shown, between what two numbers does half of the data lie? (a) 10 and 12 (c) 8 and 12 (b) 8 and 14 (d) 2 and 20 14) According to the plot shown, how many text messages are at the 75th percentile (upper quartile)? (a) 15 (c) 12 (b) 13.5 (d) 14 55

58 15) Create a box-and-whisker plot for the following set of data. Label minimum, Q1, median (Q2), Q3, and maximum. 20, 15, 45, 33, 19, 30, 31, 32, 31, 30, 27, 34, 50, 22, 29, 30 16) Make a box-and-whisker plot from the following data sets. Plot A Plot B Plot C Initial weights of 14 women in a weight loss study, in pounds (February): Weights of the same women one month later (March): Weights of the same women two months later (April): Plot A Plot B Plot C Compare the data in A and C. (a) How did the median change? (b) How did the minimum weight change? (c) How did the maximum weight change? (d) How would you judge the effectiveness of the weight loss method used in the study? 56

59 In order to pass a driver's safety course, a person must answer at least 45 out 50 questions correctly. The cumulative histogram below gives the scores of a group of people who passed the exam. 17) According to the table shown, how many total people passed the driver's safety exam? (a) 25 (c) 57 (b) 50 (d) 20 18) According to the table shown, how many people received a score of 48 or less? (a) 23 (c) 9 (b) 11 (d) 25 19) According to the table shown, how many people answered 49 questions correctly? (a) 5 (c) 9 (b) 14 (d) 41 20) The accompanying histogram shows the heights of the students in Kyra's health class. 21) The accompanying histogram shows the height distribution for students in a high school mathematics class. What is the total number of students in the class? (a) 15 (c) 209 (b) 16 (d) 5 22) Using the cumulative frequency table, how many students received a test score between a 70-79? What is the total number of students in the class? (a) 28 (c) 26 (b) 49 (d) 11 23) The test scores for 10 students in Ms. Sampson's homeroom were 61, 67, 81, 83, 87, 88, 89, 90, 98, and 100. Which frequency table is accurate for this set of data? (a) 0 (c) 80 (b) 12 (d) 26 (a) (c) (b) (d) 57

60 24) The number of calls from motorists per day for roadside service was recorded for the month of December The results were as follows: Set up a frequency table for this set of data values. Interval Tally Frequency Fill in the cumulative frequency table and create a cumulative histogram for this set of data values. Interval Cumulative Frequency 58

61 Day 8 - Chapter 10A Review Data Analysis SWBAT: Apply Their Knowledge on Data Analysis 1. According to the box-and-whisker plot shown below, what is the third quartile value? [A] 70 [B] 80 [C] 90 [D] Data regarding the students in the senior class: 578 students, 236 honor students, 150 scholarship winners, 51% male. This data can be described as being [A] qualitative [B] quantitative [C] both [D] neither 3. The correlation seen in the graph at the right would be best described as: [A] high positive correlation [B] low positive correlation [C] high negative correlation [D] low negative correlation 4. 59

62 5. 6. What is the total number of children in the families of the students in a ninth grade class? [A] 25 [B] 10 [C] 16 [D] 5 60

63 7. 8. Karen has grades of 90, 80, and 84 on three History exams. What grade must she obtain on the next test to have an average of exactly 88 for the four exams? [A] 60 [B] 88 [C] 98 [D] 95 Part II Show all work! 9. On a math test, 18 students received the following scores: 95, 90, 90, 90, 85, 85, 85, 85, 80, 80, 80, 75, 75, 75, 70, 65, 65, 55 Use the data to make a stem-and-leaf plot. 61

64 10. a. Which interval contains the median? b. Which interval contains the lower quartile? c. Which interval contains the upper quartile? a) Complete the cumulative frequency table above. b) 62