Middle Years

# 10.06 Comparing data sets

Worksheet
Comparing data sets
1

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

a

Find the total number of goals scored by both teams in Match C.

b

Find the total number of goals scored by Team 1 across all the matches.

c

Calculate the mean number of goals scored by:

i

Team 1

ii

Team 2

2

The table shows the scores of Student A and Student B in 5 separate tests:

a

Find the mean of the scores of:

i

Student A

ii

Student B

b

What is the mean of the combined scores of the two students?

c

What is the highest score overall and which student obtained that score?

d

What is the lowest score overall and which student obtained that score?

3

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

a

Copy and complete the table, giving your answers correct to two decimal place where appropriate:

b

4

A stationery shop kept a weekly record of the number of pens and notebooks sold:

a

Find the number of pens sold on Tuesday.

b

Find the number of notebooks sold on Friday.

c

Find the total number of notebooks sold during the week.

d

Find the total number of pens sold during the week

e

Find the percentage of pens sold on Thursday, rouding your answer to two decimal places.

f

Calculate the mean number of notebooks sold per day. Round your answer to one decimal place.

g

Calculate the mean number of pens sold per day. Round your answer to one decimal place.

h

5

The runs scored by each player in a cricket match are displayed below:

• Team A: \, 63, \, 0, \, 81, \, 22, \, 39, \, 66, \, 9, \,18, \, 3, \, 3, \, 5

• Team B: \, 21, \, 26, \, 18, \, 69, \, 62, \, 26, \, 5, \, 28, \, 2, \, 1, \, 2

a

Find the mean runs of the following teams, rounded to one decimal place:

i

Team A

ii

Team B

b

Which team scored more runs?

6

In a standardised test out of 100, the students in two classes got the results displayed below:

• Class A: \, 70, \, 64, \, 94, \, 78, \, 79, \, 61, \, 69, \, 93, \, 64, \, 79, \, 64, \, 71, \, 82, \, 68, \, 66

• Class B: \,86, \, 68, \, 51, \, 80, \, 63, \, 87, \, 79, \, 89, \, 62, \, 79, \, 84, \, 77, \, 67, \, 80, \, 75

a

Find the median mark for:

i

Class A

ii

Class B

b

Using the medians, which class did better on the test?

7

The monthly rainfall for two cities across a year is displayed below:

• City A: \, 122, \, 120, \, 121, \, 67, \, 79, \, 24, \, 8, \, 46, \, 27, \, 67, \, 80, \, 128

• City B: \, 51, \, 66, \, 33, \, 78, \, 79, \, 92, \, 78, \, 99, \, 41, \, 60, \, 26, \, 56

a

Find the range in monthly rainfall for:

i

City A

ii

City B

b

Which city had more consistent rainfall throughout the year?

8

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

a

What is the mean number of beans picked per day for Plant A? Round your answer to one decimal place.

b

What is the mean number of beans picked per day for Plant B? Round your answer to one decimal place.

c

What is the range for Plant A?

d

What is the range for Plant B?

e

Which plant produces more beans on average?

f

Which plant has a more consistent yield of beans?

9

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

a

Find the mean weight of the group of men.

b

Find the mean weight of the group of women.

c

Which group is heavier?

Key: 8|3 = 83

10

The stem and leaf plot shows the batting scores of two cricket teams, India and Sri Lanka:

a

Find the highest score in:

i

India

ii

Sri Lanka

b

Find the mean score of:

i

India

ii

Sri Lanka

c

Calculate the combined mean of the two teams.

Key: 8|3 = 83

11

The stem and leaf plot shows the test scores of two classes, A and B:

a

Find the highest score in:

i

Class A

ii

Class B

b

Find the mean score of:

i

Class A

ii

Class B

c

Calculate the combined mean of the two classes, correct to two decimal places.

Key: 8|3=83

12

The stem and leaf plot shows the number of books read in a year by a random sample of university and high school students:

a

Interpret the lowest score for the University students.

b

Compare the medians of both groups of students.

c

For which student group(s) is the mean greater than the median?

Key: 4 \vert 1 \vert 2 = 14 \text{ books and }12\text{ books}

13

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

a

Which group carried more cash?

b

Find the median amount of cash that the boys carried

c

Find the median amount of cash that the girls carried.

d

Which group's distribution is roughly bell shaped?

e

Which group has more variation in the amounts of cash?

f

Were there any outliers in the boys' amounts? If so, what are the value(s)?

g

Were there any outliers in the girls' amounts? If so, what are the value(s)?

Key: 1 \vert 2 \vert 2 = \$21 \text{ and } \$22

14

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

a

Who made a 14 minute phone call?

b

Who has the higher median?

c

Is Sharon's mean greater than her median?

d

Is Tricia's mean greater than her median?

Key: 2 \vert 2 \vert 6 = 22 \text{ and } 26

15

The back to back stem and leaf plot shows the number of pieces of paper used over several days by Charlie’s and Dylan’s students:

a

Did Charlie's students use 7 pieces of paper on any day?

b

Who's class had the higher median?

c

Is the median greater than the mean in both groups?

Key: 1 \vert 1 \vert 3 = 11 \text{ and } 13

16

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

a

Interpret the lowest score for Hotel A.

b

Which hotel's median is higher?

c

Is the mean greater than the median in both groups?

Key: 2 \vert 1 \vert 3 = 12 \text{ and }13

17

The median house price in Oklachusetts is \$750\,000 with a mean price of \$800\,000 and the median house price in Brockway is \$750\,000 with a mean price of \$680\,000.

Which town is most likely to have some very expensive houses? Explain your answer.

18

Two Chemistry classes, each with 15 students, sit a 10-question multiple choice test, each with four possible answers (only one of which is correct). Their class results, out of 10, are below:

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

• Class 2: \, 10, \, 6, \, 9, \, 8, \, 10, \, 9, \, 7, \, 7, \, 6, \, 8, \, 8, \, 10, \, 8, \, 9, \, 8

a

Complete the following table, rounding your answers to one decimal place when necessary:

b

Which class was more likely to have studied for their test? Explain your answer.

19

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

• Person A: \, 10, \, 9, \, 6, \, 6, \, 7, \, 8, \, 5, \, 6, \, 9, \, 9, \, 7, \, 5, \, 10, \, 9

• Person B: \, 7.5, \, 7.5, \, 8, \, 7.5, \, 7, \, 8, \, 7.5, \, 7, \, 7, \, 7, \, 7, \, 7, \, 8, \, 8

a

Complete the following table, rounding your answers to one decimal place when necessary:

b

Which person seems to be the least consistent in their sleep habits?

c

d

Which person had the most sleep over the 14 nights?

e

20

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

a

Calculate the mean for Class 1 correct to one decimal place.

b

Calculate the mean for Class 2 correct to one decimal place.

c

Find the range for Class 1.

d

Find the range for Class 2.

e

Do you think Class 1 studied for their test? Justify your answer.

f

Do you think Class 2 studied for their test? Justify your answer.

21

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

a

If the data for each restaurant was represented using a histogram, what would the likely shape of the histogram for Berger's Burgers be?

b

Which restaurant likely has the oldest employee on the night the data is recorded?

c

Which restaurant has the most employees of a similar age?

d

e

Which restaurant has an older workforce?

f

22

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

• Group 1: \, 46, \, 34, \, 35, \, 44, \, 31, \, 37, \, 38, \, 31, \, 40, \, 29

• Group 2: \, 44, \, 41, \, 40, \, 51, \, 52, \, 41, \, 36, \, 51, \, 51, \, 38

a

Calculate the range for:

i

Group 1

ii

Group 2

b

Calculate the mean, rounded to one decimal place, for:

i

Group 1

ii

Group 2

c

Do you think the two groups of birds are from the same species? Explain your answer.

23

The prices of sales at two locations of a shop are recorded in the histograms below:

a

Find the mean sale price for:

i

Location A

ii

Location B

b

c

Which location had a higher average sale price?

24

An online shopping website records the user ratings for two similar products in the histograms below:

a

Find the median user rating for:

i

Product A

ii

Product B

b

According to the website's rating system, a perfect rating is 5.0. Which product got more perfect ratings?

c

According to the website's rating system, a positive rating is greater than 3. Which product got more positive ratings?

25

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:

a

Find the mode for Group A.

b

Find the mode for Group B.

c

Find the range for Group A.

d

Find the range for Group B.

e

Which group scored the lowest total number of goals during the season?

f

Which group has the most varied results?