Question

Which of the following measures of central tendency can have more than one value?

• A. Mean
• B. Median
• C. Mode
• D. All of the above.

Answer 1

The correct option is C Mode

Consider the number of pencils sold by a shopkeeper on $5$ different days are as follows:


The mean of the given data set of number of pencils sold on 5 different days is calculated as,

$\begin{array}{cc}\text{Mean}& =\frac{\text{Sum of all data points}}{\text{Total number of data points}}\\ & =\frac{7+12+6+12+6}{5}\\ & =\frac{43}{5}=8.6\end{array}$

Thus, the mean is $8.6$, which implies the given data set has only one mean. On average, the shopkeeper sold 8.6 pencils each day.

The median of the given data is defined as the middle value of the data set, when arranged in ascending order.

Arrange the given data set in ascending value and observe the middle value.


The median of given data set is $7$, thus the median can have only one value. In case of even number of terms, the average of the middle two values is taken as median, which implies the given data set can have only one median.

The mode of the given data set is defined as the value which occurs most frequently in the given set.

Observe the given data,


Thus, there are two values which occurs twice, this implies the given data set has two values of mode, i.e., $6$ and $12$.

Hence, out of the three measures of central tendency, only mode can have more than one value.