Question

Which of the following statements are correct about mean?

• A. Mean always lies between the largest and smallest value in the given data set.
• B. Mean can be used for both numerical data set and categorical data set.
• C. Mean has to be one of the given data values.
• D. Mean of given data points is basically known as the average of the given data points.

Answer 1

Answer: (A), (D)

Mean of given data points is basically known as the average of the given data points.

Consider the given data set points $3,5,7,9,11$, and $13$. The mean of these data points is calculated as,

$\begin{array}{cc}\text{Mean}& =\frac{\text{Sum of all data points}}{\text{Total number of data points}}\\ & =\frac{3+5+7+9+11+13}{6}\\ & =\frac{48}{6}\\ & =8\end{array}$

It can be observed that the mean of the given data set points lies between the smallest and largest values, i.e., $3\le 8\le 13$ and it need not to be one of the given values.

Furthermore, mean of given data points is also known as the average of the given data points.

For categorical data, look at the following example where it is required to find the mean of different colour of shirts.

It is not possible to find the mean of the given data, as there is no numerical information given. Thus, it can be concluded that the mean can be calculated only for numerical data and not for categorical data.