Question

Which best describes the spread of a set of data that has an interquartile range of 14 and a mean absolute deviation of 6?

A.
The average distance of all data values from the mean is 10 and the middle 50% of data values has a range of 8.

B.
The average distance of all data values from the mean is 10 and the middle 50% of data values has a range of 20.

C.
The average distance of all data values from the mean is 6 and the middle 50% of data values has a range of 14.

D.
The average distance of all data values from the mean is 14 and the middle 50% of data values has a 6.

Answer 1

Hints:
1. The IQR (Interquartile range) is between the 25th and 75th percentiles, so contains the middle half (50%) of data.
2. The mean absolute deviation is the average "distance" of data from the mean.
For example, dataset
{2,3,4,12,13,14} has a mean of 8 and a mean absolute deviation of 5 because
(|2-8|+|3-8|+|4-8|+|12-8|+|13-8|+|14-8|)/6=5