Chapter 12.5, Problem 17MCQ

To determine

To find when each measure of central tendency is most useful.

Explanation of Solution

If a data set does not contain an outlier, an outlier is the data value that is much greater or less than the other values in the data set, then mean is most useful to describe the middle of the data set.

For example: let us consider a data set that does not contain an outlier.

  $8.2,9.3,8.5,8.8,9$ ................ (1)

Check the given data set (1) for an outlier. You see that there is no outlier, in the data set. So, use means to describe the middle of a set of data.

If the data set has an outlier, an outlier is the data value that is much greater or less than the other values in the data set then median is most useful to describe the middle of the data set.

For example: let us consider a data set that contains an outlier.

  $12930313333$ ................ (2)

Check the given data set (2) for an outlier. You see that the data set contain an outlier. So, use median to describe the middle of a set of data. Median is most useful to describe the middle of the data set

If the data items or the data set represent nonnumeric values or most popular items, then mode is the most useful to describe the middle of the data set..