Which measure of central tendency best represents the data? Justify your selection and then find the measure of central tendency.

Question

A company collected funds for charity from employees. The amount donated by some employees on the first day is as follows: $10, $20, $15, $100, $10, $15, $10 Which measure of central tendency best represents the data? Justify your selection and then find the measure of central tendency.

Answer 1

Order the 7 data values from low to high:

10, 10, 10, 15, 15, 20, 100.

The mean = sum of the values / n = $180 / 7 = $25.71.

The median is the number in the middle, here the 4th value, = $15.

The mode is the value that most often appears, here $10.

The mean is influenced by values considerably different in size than the rest. $100 inflates the mean, so it is not the best choice.

The median is not influenced by values considerably different in size than the rest. The median is a good choice for these data.

The mode may not be an appropriate choice because it depends on the frequency with which values appear and that frequency can be as low as 1, i.e. all values are unique, to as high as 7 (in this case) where all values are identical.

The median is the safest and best measure of central tendency because it is not as influenced by the vagaries of observed data.