7.07 Comparing data sets

Which of the following sets of data has the lowest mode:

• Set A:\,3,\, 9,\, 18,\, 9,\, 65,\, 13

• Set B:\,5,\, 12,\, 16,\, 16,\, 50,\, 3

Which of the following sets of data has the highest median:

• Set A:\,3,\, 9,\, 13,\, 18

• Set B:\,9,\, 16,\, 16,\, 65,\, 86

Which of the following sets of data has the lowest mean:

• Set A:\,14,\, 15,\, 2,\, 15,\, 26

• Set B:\,7,\, 5,\, 3,\, 2,\, 1,\, 5

Which of the following sets of data has the lowest median:

• Set A:\,14,\, 15,\, 2,\, 15,\, 26

• Set B:\,7,\, 5,\, 3,\, 2,\, 1,\, 5

Consider the following sets of data:

• Set A:\,101,\, 105,\, 118,\, 129,\, 136

• Set B:\,19,\, 23,\, 25,\, 28,\, 29

• Set C:\,22,\, 25,\, 43,\, 45,\, 57

• Set D:\,104,\, 107,\, 113,\, 128,\, 141

Which of the following dot plots has the highest median?

A

B

Which of the following dot plots has the lowest mode?

A

B

Which of the following dot plots has the smaller spread?

A

B

Do the following dot plots have the same range?

Which of the following histograms has the largest mode?

A

B

Which of the following histograms has the smallest median?

A

B

Consider the following histograms:

A

B

C

D

The number of goals scored by Team 1 and Team 2 in a football tournament are recorded in the following table:

The following table shows the scores of Student A and Student B in five separate tests:

The residents of two blocks of townhouses were asked the number of pets they own. The frequency of various responses are presented in the following dot plots:

a

Is the pet ownership a little lower or higher in Block A than Block B?

b

In Block A, how many pets do most households have?

c

In Block B, how many pets do most households have?

d

Describe the shape of the data for Block A.

e

Find the range of the number of pets in Block A.

f

Which block has more variability in the the number of pets?

g

Do either sets of scores have an outlier?

Two friends compete in a game which involves some luck in dice rolls and some skill in the strategy played. They play 10 games and their scores for each game is shown below:

• Caitlin: \,37,\, 52,\, 47,\, 43,\, 55,\, 56,\, 10,\, 46,\, 59,\, 36
• Ben: \,38,\, 62,\, 12,\, 45,\, 72,\, 21,\, 125,\, 26,\, 62,\, 50

The following histograms show the season results of two soccer groups, Group A and Group B, and the number of games (frequency) in which they scored a certain number of goals:

The beaks of two groups of bird are measured, in millimetres, to determine whether they might be of the same species. The measurements are shown below:

• Group 1: \,33,\, 39,\, 31,\, 27,\, 22,\, 37,\, 30,\, 24,\, 24,\, 28

• Group 2: 29,\, 44,\, 45,\, 34,\, 31,\, 44,\, 44,\, 33,\, 37,\, 34

Marge grows two different types of bean plants. She records the number of beans that she picks from each plant for 10 days. Her records are shown below:

• Plant A: \,10,\, 4,\, 4,\, 5,\, 7,\, 10,\, 3,\, 3,\, 9,\, 10

• Plant B: \,8,\, 7,\, 5,\, 5,\, 9,\, 7,\, 8,\, 7,\, 5,\, 6

Sarah and Georgio completed the same five exams during an exam block. Below are their results:

• Sarah: \,86,\, 83,\, 86,\, 88,\, 98

• Georgio: 61,\, 83,\, 50,\, 85,\, 83

The pulse rates of two groups are given below:

• Group 1: \,82,\, 85,\, 88,\, 65,\, 73,\, 89,\, 79,\, 90,\, 76,\, 68,\, 88,\, 65,\, 63,\, 62,\, 88,\, 82

• Group 2: \,75,\, 88,\, 74,\, 73,\, 80,\, 76,\, 67,\, 81,\, 71,\, 83,\, 89,\, 62,\, 63,\, 80,\, 71,\, 78

The ages of employees at two competing fast food restaurants on a Saturday night are recorded. Some statistics are given in the following table:

Two Science classes, each with 20 students, were given a 10 question True/False test. The results for each class are shown below:

Two English classes, each with 15 students, sit a 10 question multiple choice test. Their class results, out of 10, are below:

• Class 1: \,3,\, 2,\, 3,\, 3,\, 4,\, 5,\, 1,\, 1,\, 1,\, 4,\, 2,\, 2,\, 3,\, 3,\, 2

• Class 2: \,8, \,9, \,9, \,8, \,8, \,6,\, 8,\, 10,\, 6,\, 8,\, 8,\, 9,\, 6,\, 9,\, 9

The hours of sleep per night for two people over a two week period are shown below:

The salaries of men and women working the same job at the same company are given below:

Who seems to be getting the higher salary, the men or the women? Explain your answer.

Consider the following statistics on vehicle theft across each state in 2016 and 2017:

Consider the following statistics on road accident fatalities over a 10 year period in Australia:

The following table shows the number of units of blood donated per week over 10 weeks in two states:

The test scores of twelve students in Music and French are listed below.

• \text{ Music: }\,79,\, 59,\, 74,\, 94,\, 51,\, 71,\, 93,\, 84,\, 69,\, 61,\, 86,\, 86

• \text{ French: }\, 62,\, 71,\, 64,\, 82,\, 83,\, 99,\, 87,\, 89,\, 66,\, 73,\, 59,\, 76

Display the data in a back-to-back stem plot.

The data below represents how long each student in two different classes could hold their breath for, measured to the nearest second.

• \text{ Mrs Nguyen's class: }\, 55,\, 59,\, 61,\, 66,\, 71,\, 75,\, 80,\, 89,\, 91,\, 95,\, 101,\, 103,\, 103,\, 109,\, 111

• \text{ Miss Humphreys's class: } 51,\, 66,\, 67,\, 68,\, 77,\, 78,\, 79,\, 81,\, 83,\, 85,\, 85,\, 86,\, 92,\, 101,\, 110

Two friends have been growing sunflowers. They have measured the height of their sunflowers to the nearest centimetre, with their results shown below:

• Tricia: \,39,\, 18,\, 14,\, 44,\, 37,\, 18,\, 23,\, 28

• Quentin: \,49,\, 25,\, 42,\, 5,\, 47,\, 12,\, 15,\, 8,\, 35,\, 22,\, 28,\, 6,\, 21

The weight (in kilograms) of two groups, A and B, were recorded in a stem plot as shown.

The Cancer Council surveyed 60 random people, asking them approximately how many hours they spent in the sun in the last month. The responders were split up into two groups, tourists and local residents and the results are shown below:

The data below shows the results of a survey conducted on the price of concert tickets locally and the price of the same concerts at an international venue:

The back-to-back stem plots show the number of pieces of paper used over several days by Max’s and Charlie’s students:

The stem plot shows the test scores of a school's two Year 7 classes, A and B:

The stem plot shows the batting scores of two cricket teams, A and B:

Ten participants had their pulse measured before and after exercise with results shown in the stem plot below:

The back-to-back stem plot shows the amount of cash (in dollars) carried by a random sample of teenage boys and girls:

The following back-to-back stem plot shows the length (in minutes) of a random sample of phone calls made by Sharon and Tricia:

The back-to-back stem plot shows the number of desserts ordered at Hotel A and Hotel B over several randomly chosen days:

The weight (in kilograms) of a group of men and women were recorded and presented in a back-to-back stem plot as shown:

\text{ Key: }3 \vert 6 \vert 0 = 63 \text{ kg and } 60\text{ kg}

The test scores of 11 students in Drama and German are listed below.

• Drama: \,75,\, 85,\, 62,\, 65,\, 52,\, 76,\, 89,\, 83,\, 55,\, 91,\, 77

• German: \,82,\, 86,\, 76,\, 84,\, 64,\, 73,\, 89,\, 62,\, 54,\, 69,\, 78

Construct parallel box plots to represent both data sets.

The following box plots shows the number of points scored by two basketball teams in each of their matches:

Cooper and Marion are racing go-karts. The times (in seconds) for the 12 laps of their qualifying race are shown below:

• Cooper: \,58.9,\, 46.5,\, 52.6,\, 66.6,\, 58.4,\, 53.1,\, 45.0,\, 52.1,\, 52.4,\, 52.7,\, 44.8,\, 51.7
• Marion: \, 47.8,\, 54.6,\, 68.5,\, 68.0,\, 62.8,\, 57.2,\, 54.8,\, 63.4,\, 58.1,\, 64.3,\, 66.2,\, 47.1

Two friends compete in hammer throw competitions and train together over a season. They compete in 15 competitions and their final throw for each competition is shown below:

• Tim: \,29.8,\, 37.4,\, 33.9,\, 38.8,\, 34.3,\, 36.5,\, 34.5,\, 30.0,\, 35.2,\, 38.4,\, 33.0,\, 33.2,\, 39.6,\, 35.0,\, 36.9
• Odi: \,32.2,\, 35.4,\, 34.8,\, 33.0,\, 38.4,\, 26.0,\, 40.0,\, 37.2,\, 39.5,\, 42.4,\, 38.6,\, 42.3,\, 38.4,\, 42.8,\, 37.2

Two groups of size twelve take a test to assess their reaction time. The participants clicked a button as soon as they heard a sound which was played at random intervals. The reaction time in milliseconds of each participant is shown below:

• Group A: \,220,\, 210,\, 220,\, 215,\, 180,\, 185,\, 190,\, 190,\, 195,\, 190,\, 195,\, 195
• Group B: \,210,\, 170,\, 200,\, 170,\, 190,\, 210,\, 180,\, 200,\, 180,\, 210,\, 190,\, 190

The following boxplots summarize results from a medical study. The treatment group received an experimental drug to relieve cold symptoms, and the control group received a placebo. The boxplots show the number of days each group continued to report symptoms:

The box plots drawn below show the number of repetitions of a 70\text{ kg} bar that Weightlifter A and Weightlifter B can lift. They both record their repetitions over 30 days: