Question

The following data depicts the age of people present in the class:


With respect to this data, choose the correct following options.

• A. Miss Ellie's age will have no effect on the median of the data.
• B. Miss Ellie's age will increase the mode of the data.
• C. The mode with Miss Ellie's age is same as the mode without Miss Elllie's age.
• D. Miss Ellie's age will decrease the median of the data.

Answer 1

Answer: (A), (C)

The mode with Miss Ellie's age is same as the mode without Miss Elllie's age.

The median for the odd number of terms is the middle value of the given data, when arranged in ascending order.

And the mode is the most frequently occuring value in the given data set.

Arrange the given data in ascending order and observe the median and mode of the given data.


It can be observed that the middle value is $11$, therefore the median of given data set is $11$. Moreover, the most frequently occuring value is $11$, thus the mode is $11$.

Now observe the given data excluding Miss Ellie's age.


The median for even number of terms is the average of the middle two terms. Therefore, the median of this data set is calculated as,

$\begin{array}{cc}\text{Median}& =\frac{11+11}{2}\\ & =\frac{22}{2}\\ & =11\end{array}$

And since the most repetitive value is $11$, therefore the mode of this data set is also $11$.

Hence, Miss Ellie's age neither changes the median nor the mode of the given data set.