Question

find the mean, median, and interquartile range for the data set below. 5,8,9,11,13,15,16,17,17,18,22,23

Answer 1

Mean: 14.5

Median: 15.5

(IQR) Interquartile range: 7.5

Explanation:

Mean: 5 + 8 + 9 + 11 + 13 + 15 + 16 + 17 + 17 + 18 + 22 + 23 = 174/12 = 14.5

Median: 15.5

Lower quartile: 10

Upper quartile: 17.5

Interquartile range: 17.5 - 10 = 7.5

Answer 2

Mean: 14.5

Median: 15.5

IQR = 7.5

Explanation:

For mean:

Mean= (∑x)/n

=(5+8+9+11+13+15+16+17+17+18+22+23)/12

= 174/12

=14.5

Median:

As the data is already sorted and the number of items are odd, average of two middle values will be the median of the data.

5,8,9,11,13,15,16,17,17,18,22,23

Median=(15+16)/2

=31/2

=15.5

IQR:

For IQR, the data has to be divided in two parts, lower and upper, then we have to find the median of both parts separately. The difference of medians of both parts is called the Interquartile range.

So for lower part,

5,8,9,11,13,15

Median for lower part= (9+11)/2

= 20/2

=10

For upper part:

16,17,17,18,22,23

Median for lower part= (17+18)/2

= 35/2

=17.5

IQR=17.5-10

=7.5