Data & Statistical Analysis Chapter Questions

1. How does data help us make decisions?

2. Why are there different ways to display data?

3. What are some of the ways to display data?

4. How do people use data to mislead?

5. How can data be used to make predictions?

Data & Statistical Analysis Chapter Problems

Measures of Central Tendency Classwork

1. Which of the following data sets have outlier(s)? a. 1, 5, 7, 9, 10, 11, 15 b. 25, 39, 49, 53, 56, 60 c. 18, 19, 20, 24, 30, 60 d. 70, 74, 76, 79, 82, 83

2. Find the mean, median and mode of the following numbers:

4, 10, 11, 20, 21, 30, 9, 100, 21 Mean: Median: Mode:

3. Find the range: 30, 31, 28, 18, 30, 4, 1

4. Find the mean, median, mode, range, and outliers for the data below.

Candy Calories

Twix 291

Reeses 232

Milky Way 228

Charleston Chew 230

Runts 60

Hershey Choc. Bar 210

Butterfinger 207

Fun Dip 150

Twizzler 160

Snickers 271

Swedish Fish 150

M&M’s 243

Skittles 231

Kit Kat 218

Baby Ruth 156

5. Find the mean, median, mode, range, and outliers for the data below.

Average Rain Fall in Atlantic City Month Inches

January 3.5

February 3.1

March 3.6

April 3.6

May 3.3

June 2.6

July 3.8

August 4.1

September 2.9

October 2.8

Homework

6. Which of the following sets of data have outliers: a. 90, 92, 93, 94, 97, 100 b. 4, 20, 27, 28, 33, 34, 37 c. 64, 67, 68, 69, 73, 75, 79 d. 18, 33, 38, 39, 42, 43, 46

7. Find the mean, median, and mode for the following numbers:

5, 19, 45, 2, 4, 29, 18, 2, 7 Mean: Median: Mode:

8. Find the range: 7, 9, 17, 20, 28, 30, 31

9. Find the mean, median, mode, range, and outliers for the data below:

School Play Year Tickets Sold

1990 321

1991 370

1992 376

1993 474

1994 467

1995 474

1996 540

1997 510

1998 579

1999 603

2000 589

2001 632

2002 699

2003 730

2004 727

2005 748

10. Find the mean, median, mode, range, and outliers for the data below:

Average Temperature Trenton

Month Temperature (°F) January 30°

February 32°

March 42°

April 51°

May 62°

June 71°

July 75°

August 74°

September 67°

October 56°

Central Tendency Application Problems Classwork

11. Your test grades are 70, 85, 95, 93, and 94. You have one more test and want an average

of an 86. What must you earn on your next test?

12. Your test grades are 60, 55, 68, 78, 80, 68, and 72. To pass this class your average must be a 70 or above. You have one more test to take. Is it possible for you to pass this class? Why or why not? If you can pass the class what score must you earn on the next test?

13. Consider the following data set: 13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is 15

The mode is 13

The median is 14

What would happen if the value of 20 was added to the data set? How would the mean, median and mode change?

14. Consider the following data set: 13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is 15

The mode is 13

The median is 14

What would happen if a value “x”, was added to the set? How would the median change: If x was 16? If x was another number in the list other than 16? If x was a number not on the list?

15. Consider the data set: 70, 74, 77, 80, and 83. Identity the data values that remain the same

if the value “x”, which is less than 70, is added to the set of data.

Homework

16. Your test grades are 90, 95, 83, 89, and 91. What must you earn on the next test to receive an average of 91?

17. You are comparing grades with a friend and he tells you that you cannot earn an A in the

class. To receive an A in the class your test average must be a 93 or above. Your grades are 100, 79, 80, 92, 87, 60, and a 93. You still have one more test left. Is it possible to get an A in this class? Why or why not? If it is possible to earn an A what must you get on your next test?

18. Consider the following data set: 8, 9, 10, 10, 10, 11, 11, 11, 12, 13

The mean is 10.5

The median is 10.5

The mode is 10 and 11

What would happen if the value of 10 was added to the data set? How would the mean median and mode change?

19. Consider the following data set: 8, 9, 10, 10, 10, 11, 11, 11, 12, 13

The mean is 10.5

The median is 10.5

The mode is 10 and 11

What would happen if a value of “x” was added to the set?

How would the mean change? If x was not 12? If x was another number on the list other than 12? If x was a number not on the list?

20. Consider the data set: 48, 52, 55, 58, 60. Identify the data values that remain the same if “x”, a number greater than 55, is added to the data set. Frequency Tables & Histograms Classwork

21. The following are test grades from your classmates. Organize the data into a frequency table.

100 73 89 65 86 79 83 95 83 96 83 86 76 69 89 79 74 85

22. The following are times that it took children in gym class to run a mile. Organize this data

into a frequency table. 7:23 8:02 10:04 7:05 7:50 9:24 6:59 9:01 8:34 7:25 8:55 6:39 7:55 11:01 9:28 8:02 9:54 8:24

23. Organize this data into a histogram.

Length of walk time 21 35 48 63 67 11 19 31 43 15 44 37 42 34 69 67 Time Tally Frequency 10-19 III 3 20-29 I 1 30-39 IIII 4 40-49 IIII 4 50-59 0 60-69 IIII 4

24.

a. How many students scored below 70? b. How many students scored a 52? c. Can you determine the exact value of the test grade that was in the 60’s?

25. Create a frequency table and a histogram for the data below. Tests Score

92 84 76 75 85 97 67 48 87 93 87 88 79 68 66 100 99 79 88 81 80 79 99 91

Homework 26. The following is test scores from a math test. Organize these scores into a frequency table. 78 97 49 99 67 47 97 84 79 87 86 51 97 89 87 84 79 75 97 84 83 27. The following is temperatures in New Jersey in August. Organize them into a frequency table 100 102 105 97 95 101 89 88 90 99 95 93 89 89 96 102 91 99 98 92 103 108 98 92

28. Organize this data into a histogram.

Length of time walked 64 41 38 27 11 48 33 13 61 57 49 37 19 69 45 34 24 12

Time Tally Frequency 10-19 IIII 4 20-29 II 2 30-39 IIII 4 40-49 IIII 4 50-59 I 1 60-69 III 3

29.

A. How many students scored in the 70’s? B. How many students scored below 70? C. How many students scored 90 or above?

30. Create a histogram and a frequency table for the following data. Test Scores 92 97 98 97 85 83 97 85 84 76 79 89 99 84 86 77 51 89 83 97 92 78 85 89 Stem-and-Leaf Plots Classwork

31. Create a stem-and-leaf plot for the data. Daily temperature: 80 82 79 84 86 79 92 90 96 100 97 88 32. What is the median of the data of the following stem-and-leaf plot?

33. What is the mode of the data in the following stem-and-leaf plot?

34. Make a stem-and-leaf plot from the following data. Test scores: 87 88 89 79 57 69 68 99 91 85 89 75 89 94 92 91 84 87 35. From your stem-and-leaf plot made in #34, create a histogram. Homework 36. Create a stem-and-leaf plot for the data: Test scores: 67 89 84 95 91 97 69 76 81 73 94 74 86 81 92 76 54 60 37. What is the median of the data in the following stem-and-leaf plot?

38. What is the mode of the data in the following stem-and-leaf plot?

39. Make a stem-and-leaf plot from the following data. Time spent walking: 20 24 10 8 32 27 28 10 15 34 9 34 35 25 31 27 28 19 40. From the stem-and-leaf plot you created in #39 create a histogram, list the mode, and list the median. Box-and-Whisker Plots Classwork Test Grades: 78, 82, 65, 46, 84, 99, 100, 90, 75, 59, 75, 79, 80, 86, 68 Use the data set to 41. Create a stem and leaf 42. Identify the upper and lower extremes Find the following measures: 43. median 44. lower and upper quartiles 45. Create a box and whisker plot Homework Test Grades: 80, 81, 64, 66, 74, 98, 100, 91, 85, 89, 55, 66, 70, 84, 98 Use the data set to 46. Create a stem and leaf 47. Identify the upper and lower extremes Find the following measures:

48. median 49. lower and upper quartiles 50. Create a box and whisker plot Scatter Plots and Lines of Best Fit Classwork 51. Predict the test score of someone who spends 48 minutes studying.

52. Predict the test score of someone who spends 34 minutes studying.

53. Draw a scatter plot from the following data: Size of shoe Height (inches)

5 55 5.5 58

60

65

70

75

80

85

90

95

100

105

110

25 30 35 40 45 50 55 60

Time spent studying

test

sco

res

60

65

70

75

80

85

90

95

100

105

110

25 30 35 40 45 50 55 60

Time spent studying

test

sco

res

6 62 7 68 6.5 63

7.3 70 8 79 8.7 88 54. Consider the scatter graph to answer the following:

Which two points would give the line of best fit? A and B A and C D and B There is no pattern

55.Consider the scatter graph to answer the following: Which two points would give the line of best fit? A and B B and C C and D There is no pattern

Homework 56. Using the scatter graph, predict the mile time of someone who spends 6 hours a week training.

57. Using the scatter graph, predict the mile time of someone who spends 12 hours a week training.

58. Draw a scatter graph from the following data, Time spent studying (min) Grade

55 97 31 78 52 90 20 61 42 84 47 90 31 81

59. Consider the scatter graph to answer the following:

Which point would give the line best fit? A B C

5:55

7:07

8:19

9:31

10:43

11:55

0 5 10 15 20 25

Time spent training

Mil

e t

ime

5:55

7:07

8:19

9:31

10:43

11:55

0 5 10 15 20 25

Time spent training

Mil

e t

ime

There is no pattern

60. Consider the scatter graph to answer the following: Which two points would give the line of best fit? A and D A and C B and D There is no pattern

Determining the Prediction Equation Classwork 61.

Use the two points (7,14) and (15,27) to write an equation for the line of best fit. 62. If the prediction equation is y=.5t+60, where t represents time in minutes, what will the person get on his test if he studies for 45 minutes? 63. If the prediction equation to determine a test grade is y=.5t+60, and someone received an 80 on the test, how long did they study for? 64. Consider the scatter graph to answer the following: What is the slope of the line of best fit that passes through (3.4, 7) and (8, 3)? What is the y-intercept of the line of best fit that passes through (3.4, 7) and (8, 3)?

65. Consider the scatter graph to answer the following: The equation for the line of best fit is y = -1.06x + 10.7. Determine the value for x=15? Is this an interpolation or extrapolation?

Homework 66. Using the scatter graph below use the two points (3.4, 7) and (9, 1) to write an equation for the line of best fit.

67. If the prediction equation for a test grade is y=.52t+65, where t represents the time in minutes, what grade will someone earn if they study for 30 minutes. 68. If the prediction equation for a test grade is y=.52t+65, where t represents the time in minutes, how long did someone study for if they received an 83 on the exam? 69. Consider the scatter graph to answer the following: What is the slope of the line of best fit passing through (2.7, 11.1) and (9.4, 3.7)? What is the y-intercept of the line of best fit passing through (2.7, 11.1) and (9.4, 3.7)? Determine the value for x=5.Is this an interpolation or extrapolation?

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10

9, 1

7.5, 3.75.3, 4.2

4, 5.4

3.4, 7

3, 8.1

2, 9.2

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10

Choosing A Data Display Classwork 70. Choose the best data display to show the number of cans of soda that you drank each week for the last three months. A. histogram B. box and whisker C. frequency table D. bar graph E. circle graph F. stem-and-leaf 71. Chose the best data display to show the number of students that earned an A, B, C, D, F on their English final exam. A. histogram B. box and whisker C. frequency table D. bar graph E. circle graph F. stem-and-leaf 72. Chose the best data display to show the upper 50% of the scores on a Chemistry exam. A. histogram B. box and whisker C. frequency table D. bar graph E. circle graph F. stem-and-leaf 73. Chose the best data display to show the percent of students that earned an A, B, C, D, & F on their Earth’s Fury final exam. A. histogram B. box and whisker C. frequency table D. bar graph E. circle graph F. stem-and-leaf

74. Choose the best data display to show the interval of temperatures for 50% of the states. A. histogram B. box and whisker C. frequency table D. bar graph E. circle graph F. stem-and-leaf Homework 75. Choose the best data display to show the percent of students that earned a gold, silver, and bronze medal at the battle of classes. A. histogram B. box and whisker C. frequency table D. bar graph E. circle graph F. stem-and-leaf 76. Choose the best data display to show the upper 25% of the scores on a History exam. A. histogram B. box and whisker C. frequency table D. bar graph E. circle graph F. stem-and-leaf 77. Choose the best data display to show the number of A’s you earned each month in the past school year. A. histogram B. box and whisker C. frequency table D. bar graph E. circle graph F. stem-and-leaf 78. Choose the best data display to show the interval of grades for 20% of the students. A. histogram B. box and whisker C. frequency table D. bar graph E. circle graph F. stem-and-leaf 79. Choose the best data display to show the percent of students who prefer orange juice, cranberry juice, apple juice, or soda. A. histogram B. box and whisker C. frequency table D. bar graph E. circle graph F. stem-and-leaf Misleading Graphs Classwork

80. If you owned stock in M&M’s candy, which graph would you want placed on a billboard?

Percentage of Mrs. Smith’s Students’ Candy Preference

Homework 81. How can the makers of Crest change the graph so that the consumer thinks that far more people purchased Crest than Aquafresh?

M&M's38%

Almond Joy22%

Mounds25%

Reese's15%

M&M's

Almond Joy

Mounds

Reese's

38

2225

15

0

10

20

30

40

M&M's AlmondJoy

Mounds Reese's

0

100

200

300

400

500