4.045 Interquartile range

For each set of scores, find:

For each set of data, find the following:

a

b

c

	Leaf
6	2\ 7
7	1\ 2\ 2\ 4\ 7\ 9
8	0\ 1\ 2\ 5\ 7
9	0\ 1

Key: 5|2=52

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

a

b

c

d

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

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.

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:

Consider the scores displayed in the following column graph:

Class	Class centre	Frequency
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

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

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

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

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

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.

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.

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 change?

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 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 data set has the following known statistics:

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