Download Mathematics Higher - Interquartile range

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Interquartile range
Range and interquartile range are measures of spread. They tell you how spread out data is.
Quartiles divide a data set into four equal parts.
Half of the values lie between the lower
n1
Q1 _____th value,
4
where n number
of data values
quartile and the upper quartile.
Interquartile range (IQR)
Smallest
value
Lower
quartile (Q1)
Median
(Q2)
Upper
quartile (Q3)
Range largest value – smallest value
Interquartile range (IQR) upper quartile (Q3) – lower quartile (Q1)
Alison recorded the heights, in cm, of some tree
saplings. She put the heights in order.
21 23 23 25 26 26 31 32
33 35 36 40 40 41 42
Work out the interquartile range of Alison’s data.
(3 marks)
n 15
15 1
n 1 _____
_____
4
4
4
Q1 4th value 25 cm
3(15 1)
3(n 1) ________
_______
12
4
4
Q3 12th value 40 cm
IQR Q3 Q1 40 25 15 cm
Largest
value
3(n 1)
Q3 _______ th value
4
you
To work out the interquartile range,
the
need to know the lower quartile and
upper quartile.
es, n.
1. Count the total number of valu
d in
2. Check that the data is arrange
order of size.
n __1
___
3. Find the 4 th data value.
This is the lower quartile (Q1).
1)_
3(n___
___
th data value.
4. Find the
4
This is the upper quartile (Q3).
m the
5. Subtract the lower quartile fro
ile
rqu
upper quartile to find the inte art
range.
Golden rule
Always arrange the data in order of size before calculating the median or quartiles.
If the data is given in an ordered stem-and-leaf diagram then it is already in order of size.
0 | 9 represents £9
This stem-and-leaf diagram shows
the costs, in £, of some DVDs.
0 7 9 9
There are 11 pieces
There are 11 pieces of data
of data, so the
This
1 0 0 2 3 5 7
median is the
in this stem-and-leaf diagram. is the
2 0 5
6th value.
stem.
Henry measures the heights of some plant seedlings for an
experiment. This stem-and-leaf diagram shows his results.
(a) How many plant seedlings did Henry measure? (1 mark)
(b) Work out the median height.
(2 marks)
(c) Work out the interquartile range of this data. (3 marks)
112
The median is £12.
Key: 1 | 5 £15
4
5
6
7
0 2 4 4 5 9
1 3 3 4 7 8 9
2 2 5 6 8
1
Key: 5 | 3 means 5.3 cm