Which side does the mean lean?

The idea

When data is balanced or uniformly spread, the mean and median are close; an outlier at the lower end shifts the mean below the median, and one at the higher end shifts it above.

A visitor joins the family

Yaangba’s family has six members. Their mean height (164.3 cm) and median (164.5 cm) are almost the same. Now a visitor joins them.

If the visitor is very, very tall, where will the mean move compared with the median?

• The mean moves above the median
• The mean moves below the median
• Nothing changes

Change the visitor

Move the red dot to a very short, a middle and a very tall height. Watch where the mean (orange) is compared with the median (green).

The mean leans towards the outlier

With a visitor like the rest, the mean and median stay close. A very short visitor drags the mean below the median. A very tall visitor drags it above.

The mean is pulled towards the side where the outlier is.

When data is balanced or uniformly spread, the mean and median are close. An outlier at the lower end shifts the mean below the median, and one at the higher end shifts it above.

• Data | Mean | Median
• Yaangba’s family | 164.3 | 164.5
• Poovizhi’s family (low outlier) | 160.2 | 170
• A class (outlier 40) | 9.3 | 6

Notes

When data is balanced or uniformly spread, the mean and median are close. An outlier at the lower end shifts the mean below the median, and one at the higher end shifts it above.

Check yourself

Most dots in a dot plot are bunched together and one dot is far to the right. How is the mean compared with the median?

For the newspaper pages 16, 18, 20, 22, 26, 16, 10 the mean is 18.3 and the median is 18. What does this tell us?

Poovizhi’s family has mean 160.2 cm and median 170 cm. By how many cm is the median above the mean? Type a decimal.

Answer: 9.8 cm

170 − 160.2 = 9.8 cm.

The mean of a data set is less than its median. Where is the outlier?

• The mean is more than the median. — correct. Yes! The high outlier pulls the mean up, towards the right.
• The mean is less than the median.. The mean leans towards the outlier. The outlier is on the right, so the mean moves right.
• They are always equal.. They are equal only for very balanced data.
• There is a high outlier.. A high outlier would make the mean much bigger than the median.
• The data is balanced: no outlier pulls the mean far from the median. — correct. Yes! Mean and median are close, so the values are spread fairly evenly.
• There is a low outlier.. A low outlier would make the mean much smaller than the median.
• At the higher end of the data. A high outlier pulls the mean up, making it more than the median.
• At the lower end of the data — correct. Yes! A low outlier pulls the mean down, below the median.
• There must not be any outlier. A mean clearly below the median is a sign of a low outlier.