Question

Choose the correct options with respect to the mean of the data.

• A. It is the most frequently occuring value in the data set.
• B. It is the sum of all the data points divided by the total number of data points.
• C. It lies between the smallest and the largest value of the data set.
• D. The data set can have two values of mean.

Answer 1

Answer: (B), (C)

It lies between the smallest and the largest value of the data set.

The most frequently occuring value in the data set is known as the mode of the data set.

Mean, on the other hand, is defined as,

$\text{Mean}=\frac{\text{Sum of all the data points}}{\text{Total number of data points}}$

Consider the following data which depicts the height of a group of $6$ friends.


Their mean height will be calculated as,

$\begin{array}{cc}\text{Mean height}& =\frac{145+149+146+147+144+146}{6}\\ & =\frac{877}{6}\\ & =146.16\end{array}$

Thus, the mean of this data set is $146.16\text{cm}$ and it lies between the lowest and highest value of the data set, i.e., $144<146.16<149$.

Also, it can be concluded that the data set cannot have two values of mean.

So, the second and third options are correct.