Everything Maths Grade 10

Step 2: Find the quartiles

Since the data have been grouped, they have also already been sorted. Using the percentile formula and the

fact that there are 100 learners, we can find the rank of the 25 th, 50 thand 75 thpercentiles as

r 25 =

25

100

(1001) + 1

=24,75

r 50 =

50

100

(1001) + 1

=50,5

r 75 =

75

100

(1001) + 1

=75,25

Now we need to find in which ranges each of these ranks lie.

• For the lower quartile, we have that there are2 + 5 = 7learners in the first two ranges combined and
  2 + 5 + 18 = 25learners in the first three ranges combined. Since 7 < r 25 < 25 , this means the lower
  quartile lies somewhere in the third range: 30 x < 40.


• For the second quartile (the median), we have that there are2+5+18+22 = 47learners in the first four
  ranges combined. Since 47 < r 50 < 65 , this means that the median lies somewhere in the fifth range:
  50 x < 60.


• For the upper quartile, we have that there are 65 learners in the first five ranges combined and65+13 = 78
  learners in the first six ranges combined. Since 65 < r 75 < 78 , this means that the upper quartile lies
  somewhere in the sixth range: 60 x < 70.

Step 3: Find the 30 thpercentile

Using the same method as for the quartiles, we first find the rank of the 30 thpercentile.

r=

30

100

(1001) + 1

=30,7

Now we have to find the range in which this rank lies. Since there are 25 learners in the first 3 ranges combined

and 47 learners in the first 4 ranges combined, the 30 thpercentile lies in the fourth range: 40 x < 50

Ranges EMA7B

We define data ranges in terms of percentiles. We have already encountered the full data range, which is simply
the difference between the 100 thand the 0 thpercentile (that is, between the maximum and minimum values
in the data set).

DEFINITION: Interquartile range

The interquartile range is a measure of dispersion, which is calculated by subtracting the first quartile (Q 1 ) from

the third quartile (Q 3 ). This gives the range of the middle half of the data set.

DEFINITION: Semi interquartile range

The semi interquartile range is half of the interquartile range.

Chapter 10. Statistics 377