Question

Jesse asked how many magazine subscriptions each

house on his street had. These numbers are shown. What
is the interquartile range of the data set?
1, 0, 2, 3, 4, 1, 0, 0, 4, 1, 2, 2, 1

Answer 1

Interquartile range of the data is:

IQR = 2

Explanation:

First lets rearrange the data in ascending order:

0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4

Find Median:

Median = (No. of terms +1) / 2 (when n = odd number)

Median = 14/2 (th term)

Median = 7th term

Median = 1

Find Upper and Lower Medians:

As the number of total terms is odd (n=13) , we omit the median and form upper and lower sets and find their medium

0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4

Remove the median

0, 0, 0, 1, 1, 1 | 2, 2, 2, 3, 4, 4

Calculate the median of lower portion

0, 0, 0, 1, 1, 1

For even numbers

Lower Median = (0+1)/2

Lower Median = 0.5

Calculate the median of upper portion

2, 2, 2, 3, 4, 4

Upper Median = (2+3)/2

Upper Median = 2.5

Interquartile Range:

It is the difference between Upper and Lower Median

IQR = 2.5 - 0.5

IQR = 2