topic badge

9.045 Interquartile range

Worksheet
Interquartile range
1

For each set of scores, find:

i

The total number of scores

ii

The median

iii

The range

iv

The first quartile

v

The third quartile

vi

The interquartile range

a

13,\, 15,\, 5,\, 16,\, 7,\, 20,\, 12

b

- 3 ,\, - 3 ,\, 1,\, 9,\, 9,\, 6,\, - 9

c

33,\, 38,\, 50,\, 12,\, 33,\, 48,\, 41

d

1.2,\, 2.9,\, 3.5,\, 1.6,\, 3.2,\, 4.8,\, 1.9

e
Leaf
22\ 5\ 6\ 7\ 9
30\ 0\ 5\ 6\ 8
40\ 0\ 1\ 8\ 9

Key: 5|2=52

f
ScoreFrequency
53
133
162
282
313
384
482
2

For each set of data, find the following:

i

The first quartile

ii

The third quartile

iii

The interquartile range

a
b
c
Leaf
62\ 7
71\ 2\ 2\ 4\ 7\ 9
80\ 1\ 2\ 5\ 7
90\ 1

Key: 5|2=52

3

For each data set represented by a dot plot below, find:

i

The median

ii

The first quartile

iii

The third quartile

iv

The interquartile range

a
b
c
d
4

Edward records the number of fish he catches for each fishing trip over a period of time:

a

How many fishing trips did he go on?

b

Find the range.

c

Find the median.

d

Find the first quartile.

e

Find the third quartile.

f

Find the interquartile range.

5

Consider the set of scores displayed in the following column graph:

a

Complete the given frequency table:

\text{Score} \left(x\right)\text{Frequency} \left(f\right)f x
20
30
40
50
60
\text{Totals}
b

Find the median score.

c

Find the first quartile.

d

Find the third quartile.

e

Find the interquartile range.

6

A group of students were asked how many phone calls they had made the previous day. The information was collected in the given frequency table:

a

How many students were surveyed?

b

Find the range of the data.

c

Find the median of the data.

d

Find the first quartile.

e

Find the third quartile.

f

Find the interquartile range.

Phone callsFrequency
08
15
210
36
46
57
63
72
7

A sample of boxes of matches were selected for quality control and the number of matches in each box recorded in the given frequency table:

a

How many matchboxes were sampled?

b

Find the range of the data.

c

Find the median.

d

Find the first quartile.

e

Find the third quartile.

f

Find the interquartile range.

MatchesFrequency
451
462
475
483
497
5025
516
522
8

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:

a

Find the interquartile range for the international venue.

b

Find the interquartile range for the local venue.

c

At which venue is there the least spread in the middle 50\% of prices?

InternationalLocal
9\ 9\ 968
8\ 5\ 5\ 5\ 3\ 075\ 6\ 6\ 9\ 9
8\ 4\ 3\ 2\ 1\ 082\ 2\ 6\ 6
5\ 3\ 2\ 090\ 0\ 1\ 4\ 5\ 6\ 8
5100\ 3\ 5

Key: 9|6|8 = \$ 69 \text{ and } \$ 68

Estimate range and IQR
9

Consider the scores displayed in the following column graph:

ClassClass centreFrequency
1-5
6-10
11-15
16-20
a

Complete the given frequency table.

b

Use the class centres to estimate the:

i

Range

ii

First quartile

iii

Third quartile

iv

Interquartile range

10

The histogram below displays the speeds of balls delivered by a bowler in cricket:

a

Create a frequency table for the data and include a column for class centres.

b

Use the class centres to estimate the:

i

Range

ii

First quartile

iii

Third quartile

iv

Interquartile range

11

The following histogram shows the heights of tomato plants in a greenhouse:

a

Create a frequency table for the data and include a column for class centres.

b

Use the class centres to estimate:

i

The range

ii

The interquartile range

12

In a survey, the mass (in grams) of 30 individual apples from an orchard were noted and recorded in the following list:

86,\quad 87,\quad 91,\quad 93,\quad 94,\quad 95,\quad 96,\quad 96,\quad 98,\quad 99

100,\quad 101,\quad 102,\quad 103,\quad 103,\quad 104,\quad 104,\quad 105,\quad 106,\quad 106

106,\quad 107,\quad 107,\quad 107,\quad 108,\quad 108,\quad 109,\quad 109,\quad 109,\quad 109

a

Use the raw scores to find the following:

i

The range

ii

The interquartile range

b

Complete the given frequency table.

c

Using the class centres, find an estimate for:

i
The range
ii
The interquartile range
d

How much less was the approximation for the IQR than the actual IQR?

\text{Weight (g)}\text{Class} \\ \text{centre}\text{Frequency}
85\leq x \lt 9087.5
90\leq x \lt 953
95\leq x \lt 100
100\leq x \lt 105
105\leq x \lt 110
Applications
13

If there are 78 scores in a set of data, in which position will the lower quartile lie?

14

In competition, a diver must complete 8 rounds of dives. Her scores for the first 7 rounds are:

7.3, \, 7.4, \, 7.7, \, 8.4, \, 8.7, \, 8.9, \, 9.4

Determine her score in the 8th round if the upper quartile of all of her 8 scores is 8.85.

15

In a competition, a contestant must complete 12 challenges earning as many points as possible. Her scores for the first 11 challenges are:

32,\, 38,\, 45,\, 55,\, 66,\, 86,\, 94,\, 98,\, 106,\, 108,\, 117

Find her score in the 12th round if the lower quartile of all of her 12 scores is 47.5.

16

Consider the set of data:1,\, 2,\, 2,\, 4,\, 4,\, 5,\, 6,\, 6,\, 8,\, 8,\, 8,\, 9,\, 9

If one score of 8 is changed to a 9, which measure(s) of centre or spread would be altered?

17

The following set of scores has a mean of 8.4, mode of 9, median of 9, range of 11 and IQR of 7.5:

4, 5, 9, 9, 15

a

Add 10 to each score and write the new list of scores.

b

For the new set of scores find:

i

Mean

ii

Mode

iii

Median

iv

Range

v

IQR

c

Compare the measures with the statistics for the original set and hence explain which statistical measures have been affected by adding 10 to each score.

d

Multiply each original score by 10 and repeat parts (a) and (b) above for the new set of scores.

Hence explain which statistical measures have been affected by multiplying each score by 10.

18

A data set has a mean of 6 and interquartile range of 2.5.

State the new mean and interquartile range if the scores are:

a

Increased by 5.

b

Multiplied by 5.

19

A data set has the following known statistics:

MedianModeRangeInterquartile range
128187

Find the new value for each of the statistics above, given each value of the data set was:

a

Increased by 6.

b

Multiplied by 3.

c

Decreased by 4.

d

Divided by 2.

Sign up to access Worksheet
Get full access to our content with a Mathspace account

Outcomes

2.1.12

interpret statistical measures of spread, such as: the range, interquartile range and standard deviation

What is Mathspace

About Mathspace