a) For the following data set:

Question

7 9 2 5 4 11 1 4 40

Find:

i) the range. ii) the interquartile range

b) Which of the two measures calculated in part (a) is the best representation of

the spread of this data? Give a reason for your answer.

Answer 1

a)

i) The range is the difference between the highest number in the data set, and the smallest.

So,

40 - 1 = 39

ii) The interquartile range (IQR) is the difference in medians. First, organize your data from least to greatest like this:

1, 2, 4, 4, 5, 7, 9, 11, 40

Then we find the median:

1, 2, 4, 4, 5, 7, 9, 11, 40

Now we are going to find the median for the upper and lower sets.

First, omit the first median you found (5):

1, 2, 4, 4, 5, 7, 9, 11, 40

And then split the data up into two parts, divided where the five used to be:

1, 2, 4, 4 7, 9, 11, 40

Find the median of the lower portion:

1, 2, 4, 4

Find the average:

(2+4)/2=3

Now do the same for the upper values:

7,9,11,40

(9+11)/2=10

Finally, find the difference between these two values:

10-3=7

b) I believe that the IQR is a much better representation of the data because 40 is an outlier and skews the first measure when finding a regular median.