Question

A set of data has MAD 0, and one of the data values is 14. What can you say about the data values?

a) All data values are 14.
b) The data values are perfectly centered around the mean.
c) There is no variability in the data.
d) The data set is too small to make any conclusions.

Answer 1

If a data set has a MAD of 0 and one value is known to be 14, it means all data values are 14, and there is no variability within the data set.

Step-by-step explanation:

When a set of data has a Mean Absolute Deviation (MAD) of 0, this indicates that there is no variability in the data. Each data value is the same distance from the mean, which in this case is zero. Therefore, the data values are all the same. Given that one of the data values is 14, we can conclude that all data values must be 14 in order to have a MAD of 0. This is similar to a situation where the standard deviation is zero, indicating uniformity in data values.