When the mean misleads

Poovizhi's family heights average 160.2 cm, and Yaangba's average 164.3 cm. So Yaangba's family is taller — except that most members of Poovizhi's family are in fact taller than most of Yaangba's.

How can that be? Because one child in Poovizhi's family is much younger and not nearly as tall as the rest. That single small value has pulled the mean down so far that 160.2 cm is less than the heights of FOUR of the five members. Here the average does not represent the data very well.

Is there another number that would represent it better? One way is to SORT the data and pick the number in the middle. That number is called the MEDIAN (in Hindi, माध्यिका) — simply the middle value.

Sort Poovizhi's family heights: 118, 165, 170, 173, 175. The middle number is 170, so the median height is 170 cm — which describes the family far better than 160.2.

What if there is no single middle number? Yaangba's family has six members: 155, 160, 164, 165, 169, 173. With an even count there are two middle values, so we take their average: (164 + 165) ÷ 2 = 164.5 cm.

The value causing the trouble has a name. In Poovizhi's family the youngest child's height is quite different from the rest, and such a value is called an OUTLIER — a value that significantly deviates from the rest of the data.

Compare the two families now. Yaangba's data has no outlier, and its mean (164.3) and median (164.5) are close together. Poovizhi's data has one, and its mean (160.2) is far below its median (170). That gap between mean and median is itself a signal that an outlier is at work. Try recomputing Poovizhi's mean and median WITHOUT the 118 and see how much each moves.