121k views
5 votes
Consider the following set of data: 3, 6, 8, 15, 21, 22, 23 Define what is meant by “ measures of variation”. What is the interquartile range of data? What is the mean absolute deviation of the data?

1 Answer

4 votes

Answer:

Below.

Explanation:

A measure of variation is an estimate of the spread of the numbers.

For example the set of numbers 1 2 3 19 78 has a greater measure of variation than the set 1 2 3 5 9.

The interquartile range and the mean absolute deviation are measures of variation.

3 6 8 15 21 22 23

The median of the data is the middle number 15..

The lower quartile is 6 and the higher quartile is 22

The interquartile range is 22 - 6 = 16.

The mean absolute deviation (M.A.D.) is calculated as follows:

Mean = (3+6+8+15+21+22+23) / 7 = 98/7

= 14.

List the absolute differences from the mean

14 - 3 = 11

14-6 = 8

15-14 = 1

21-14= 7

22-14 = 8

23-14 = 9 ( all these have to be positive)

The sum of the differences is 11+8+1+7+8+9 = 44

So the MAD = 44/7 = 6.3 to nearest tenth.

User Vlee
by
7.0k points