Mode and comparing the averages

The mode (written Z or M₀) is the value that occurs most often.

Example: in the series 12, 25, 31, 25, 40, 25, 18, the value 25 occurs three times, so the mode is 25. A series with one mode is unimodal.

If two values are equally the most frequent, the series is bimodal; with more than two, multimodal. And some series have no mode at all, if no value repeats.

How do the three averages compare?

• In a normal distribution, shown by a symmetrical, bell-shaped curve, the mean, median and mode all coincide at the centre.
• In skewed (lopsided) data, they separate: the mean is pulled furthest towards the long tail, the mode stays at the peak, and the median lies between them.