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11.03 The spread of data sets

Worksheet
Spread of data sets
1

Calculate the range of the following sets of data:

a
22, 35, 20, 21, 40, 32
b
20, 17, 19, 18, 24, 21, 25, 22
c
30.1, 4.7, 14.6, 45.2, 11.3
d
9.75, 45.5, 30.25, 17.5, 42.75, 37.5, 16.25
2

Calculate the interquartile range of the following sets of data:

a
21, 17, 16, 18, 22, 25, 15, 20
b
21, 39, 23, 32, 22, 31, 33
c
31, 30, 25, 28, 37, 39, 20, 38, 35, 24
d
23.5, 38, 25.5, 29.5, 24, 35.5, 26.5, 20
Match box plots to graphs
3

Construct a box plot for each of the following histograms:

a
b
c
d
e
f
g
h
i
j
4

Match the histograms on the left to the corresponding box plots on the right:

Histogram A

Box Plot 1
0
1
2
3
4
5
6
7
8
9
10

Histogram B

Box Plot 2
0
1
2
3
4
5
6
7
8
9
10

Histogram C

Box Plot 3
1
2
3
4
5
6
7
8
9

Histogram D

Box Plot 4
0
1
2
3
4
5
6
7
8
9
10
Parallel box plots
5

Two groups of people, athletes and non-athletes, had their resting heart rate measured. The results are displayed in the following pair of box plots:

a

Find the median heart rate of athletes.

b

Find the median heart rate of the non-athletes.

c

Using this measure, which group has the lower heart rates?

d

Find the interquartile range of the athletes' heart rates.

e

Find the interquartile range of the non-athletes' heart rates.

f

Using this measure, which group has more consistent heart rate measures?

Athletes
40
50
60
70
80
90
Non-athletes
40
50
60
70
80
90
6

At every training session of the season, a cyclist measured her pulse rate before a sprint and after a sprint. The before and after rates, measured in beats per minute (bpm), recorded throughout the season are presented in the following box plots:

a

How much greater was her median pulse rate after the sprint than before the sprint?

b

Find the interquartile range of her pulse rate before the sprint.

c

Find the interquartile range of her pulse rate after the sprint.

d

Find the range of her pulse rate before the sprint.

e

Find the range of her pulse rate after the sprint.

f

Are her pulse rate readings more consistent before or after the sprint?

g

In the last session of the season, the cyclist recorded her highest pulse rate of the season both before and after the sprint. By how much did her pulse rate increase during this particular training session?

Pulse Rate Before (bpm)
60
70
80
90
100
110
120
130
140
Pulse Rate After (bpm)
60
70
80
90
100
110
120
130
140
7

Two weightlifters both record their number of repetitions with a 70 \text{ kg} bar over 30 days. The results are displayed in the following box plots:

a

Which weightlifter has the more consistent results?

b

Determine which of the following statistics supports your answer:

A

The mean.

B

The range.

C

The mode.

D

The graph is positively skewed.

c

Which statistic is the same for each weightlifter?

d

Which weightlifter can do the most repetitions of 70 \text{ kg}?

8

The parallel box plots below shows the data collected by the manufacturers on the life-span of light bulbs, measured in thousands of hours:

a

Complete the following table using the two box plots:

Manufacturer AManufacturer B
Median
Lower quartile
Upper quartile
Range
Interquartile range
b

Hence, which manufacturer produces light bulbs with the best lifespan? Explain your answer.

9

A class took an English test and a Mathematics test. Both tests had a maximum possible mark of 20. The following parallel box plots shows the results of the tests:

a

Complete the following table using the two box plots:

EnglishMathematics
Median
Lower quartile
Upper quartile
Range
Interquartile range
b

In which test did the class tend to score better marks? Explain your answer.

10

A mathematics test is given to two classes. The marks out of 20 received by students in each class are represented in the following box plots:

a

Complete the following table:

Class 10PClass 10Q
Median
Lower quartile
Upper quartile
Range
Interquartile range
b

Which class tended to score better marks? Explain your answer.

Class 10P
0
2
4
6
8
10
12
14
16
18
20
Class 10Q
0
2
4
6
8
10
12
14
16
18
20
11

The following box plots represent the daily sales made by Carl and Angelina over the course of one month:

Angelina's sales
0
10
20
30
40
50
60
70
Carl's sales
0
10
20
30
40
50
60
70
a

Calculate the range for Angelina's sales.

b

Calculate the range for Carl’s sales.

c

By how much did Carl’s median sales exceed Angelina's?

d

Considering the middle 50\% of sales, which salesperson had the more consistent number of sales?

e

Which salesperson had a more successful sales month?

12

The parallel box plots shows the prices, in dollars, of the items on the menu of an upmarket restaurant and the menu of a fast food restaurant:

a

Which restaurant has the higher median price for the items they sell?

b

What is the difference between the median prices of the items sold by each restaurant?

c

Which restaurant has a greater price range for the items on the their menu?

d

What is the price difference between the most expensive items sold by each restaurant?

e

What amount of the cheapest item at the fast food restaurant could be bought for the same price of the most expensive item at the upmarket restaurant?

13

The parallel box plots show the number of goals scored by two football players in each season:

a

Who scored the most goals in a season?

b

How many more goals did Holly score in her best season compared to Sophie in her best season?

c

What is the difference between the median number of goals scored in a season by each player?

d

What is the difference between the interquartile range for both players?

14

The parallel box plots shows the distances, in centimetres, jumped by two high jumpers:

a

Who had a higher median jump?

b

Who made the highest jump?

c

Who made the lowest jump?

15

Two bookstores recorded the selling price of all their books. The results are presented in the parallel box plots:

a

Which bookstore had the more consistent prices? Explain your answer.

b

Comparing the most expensive books in each store, how much more expensive is the one in store B?

c

State whether the following statements are true or false:

i

25\% of the books in Bookstore B are at least as expensive than the most expensive book in Bookstore A.

ii

25\% of the books in Bookstore B are cheaper than the cheapest book in Bookstore A.

16

A builder can choose between two different types of brick that are coloured red or yellow. The following parallel box plots shows the results of tests on the strength of the bricks:

a

Using the box plot, explain why a builder might to prefer to use the red bricks.

b

Using the box plot, explain why a builder might to prefer to use yellow bricks.

17

A cinema is showing three films, labelled A, B and C. The ages of people watching each of the films are illustrated in the parallel box plots:

a

Which film do you think has an adults only rating, restricting it to viewers 18 years of age and older? Explain your answer.

b

Which film would you recommend for a group of 15 year olds to watch? Explain your answer.

c

Which film would you recommend to a family of two parents in their 40's and two teenagers? Explain your answer.

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Outcomes

VCMSP351

Compare shapes of box plots to corresponding histograms and dot plots and discuss the distribution of data

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