Question

Which measure of central tendency is better for a data set having outlier(s)?

• A. Mean
• B. Median
• C. Mode
• D. None of the above.

Answer 1

The correct option is B Median

Consider the following data set: $1,5,4,4,4,7,9,9,56$

Here, $30$ is an outlier as it is quite large compared to other numbers.

Mean with outlier
$=\frac{\text{Sum of all the data points}}{\text{Total number of data points}}$
$=\frac{1+5+4+4+4+7+9+9+56}{9}$
$=\frac{99}{9}$
$=11$

Mean without outlier
$=\frac{\text{Sum of all the data points without outlier}}{\text{Total number of data points without outlier}}$
$=\frac{1+5+4+4+4+7+9+9}{8}$
$=\frac{43}{8}$
$=5.375$

Mean without an outlier is almost half than the mean with an outlier.
Also, the mean without outlier is around the numbers in the dataset without the outlier.

To determine the mode, arrange the numbers in ascending order: $1,\underset{–}{4},\underset{–}{4},\underset{–}{4},5,7,9,9,56$

Mode is the most repeated data point, i.e., 4

$\therefore$ If mode is the number that lies on the extreme left or extreme right of the arranged data set, we do not get an idea of other data points.
Hence, mode is not the preferred measure of central tendency when outliers are present.

For $10$ number of data points, the median is the fifth data point, i.e., $5.$

$\therefore$ The median is often the preferred measure of central tendency because the median is more resistant to outliers than the mean and mode.