Question

Smith went to an icecream parlour. He noticed that all the icecream flavours are within the range of $\$4$ of one another, except one flavour which is quite expensive than the rest. Which measure of central tendency will be most affected by that expensive flavour?

• A. Only mode
• B. Only mean
• C. Both mode and mean
• D. Neither mode nor mean

Answer 1

The correct option is B Only mean

Consider the price of various icecream flavours be given as:


The outlier is that value of the data set which is very different from the rest of the values. Thus, for the given data set, the outlier is $40$.

Now, since the mode is the most frequently occuring value of the given data set, therefore the mode of this data set is $26$.

The mean of the data set is calculated as,

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

Thus, the mean of the given data with and without outlier will be given as,

$\begin{array}{cc}\text{Mean with outlier}& =\frac{20+22+24+26+26+28+40}{7}\\ & =\frac{186}{7}\\ & =26.57\\ & \\ \text{Mean without outlier}& =\frac{20+22+24+26+26+28}{6}\\ & =\frac{146}{6}\\ & =24.33\end{array}$

Hence, the value of mode with and without outlier remains same for the given data but the value of mean changes, i.e., the mean will be most affected by that expensive flavour.