Question

Why is the mean, but not median nor mode, affected by the outliers in a data-set?

Answer 1

Mean:

The average of all the numbers in the given data is the mean.

Median:

The middle number in the given data when arranged in increasing order is the median.

Mode:

The number that occurs more frequently or repeatedly in the given data is the mode.

Outliers:

The number which is very small or very large than the other numbers in the given data is the outlier in the data set.

There may be one or more outliers in a data set or sometimes no outliers in the data set.

Outlier is an extreme value in the data set.

Effect of outliers:

The outlier can affect the mean value more than the median and mode.

This can be explained by the following example.

Consider the data as $21,23,24,23,22,23,70$.

Considering the outlier of the data set:

$\Rightarrow \mathrm{Outlier}=70$

$$\begin{gathered} \Rightarrow \mathrm{Mean}=\frac{21+23+24+23+22+23+70}{7} \\ =29.43 \end{gathered}$$

The increasing order of the data is $21,22,23,23,23,24,70$.

$\Rightarrow \mathrm{Median}=23$

$\Rightarrow \mathrm{Mode}=23$

Without considering the outlier in the given data:

The data is $21,23,24,23,22,23$.

$$\begin{gathered} \Rightarrow \mathrm{Mean}=\frac{21+23+24+23+22+23}{6} \\ =23 \end{gathered}$$

The increasing order of the data is $21,22,23,23,23,24$.

$\Rightarrow \mathrm{Median}=23$

$\Rightarrow \mathrm{Mode}=23$

The median and mode are the same in both cases.

This clearly proves that the outlier does not affect the median and mode.

Hence, the mean value is increased if the outlier is much greater than the other numbers in the data set.

The mean value is decrease if the outlier is much lesser than the other numbers in the data set.