# Comparing mean, median and mode

Example 1

Statistics from a call centre may help you understand the differences between mean, median and mode more easily.

The mean telephone call was normally around 30 seconds long.

The median telephone call was normally around 40 seconds long.

The modal (mode) telephone call was normally less than 5 seconds in length.

We can split these phone calls into three types to help explain these figures.

1.  Very short

A failed call. Many calls were answered by a voicemail message lasting only a few seconds. This can cause a modal call length of  around two or three seconds.

2.  Brief

Some calls were answered and then the recipient realised it was a telemarketing call, and so they hung up. This resulted in a large volume of brief phone calls in the middle (median) of an ordered list of call lengths (but still a smaller figure than the very short failed calls resulting from being answered by voice messages).

This man is having a brief telephone call.

3.  Conversation

Well, people can talk for quite a while once a conversation is struck up. These long conversation calls are the least frequent type of call, but their very long duration can skew the mean average length to be much higher. The calls are long but infrequent, so they don’t affect the median or the mode at all.

Long conversation phone calls can bore you to death at times.

A graph depicting this data would show a huge peak between one and ten seconds, resulting from the very short failed calls, and a slightly smaller peak between 35 and 50 seconds, resulting from the brief calls. After that, it tails off.