Question

The cups of hot chocolate consumed by $6$ owls are given as:

If Alex's consumption is ignored, then which of the following statement will be correct?

• A. Median of the number of cups of hot chocolate consumed will increase.
  
• B. Mode of the number of cups of hot chocolate consumed will remain the same.
• C. Mean of the number of cups of hot chocolate consumed will increase.

Answer 1

The correct option is B Mode of the number of cups of hot chocolate consumed will remain the same.

Below is the given data set for the number of cups of hot chocolate consumed by 6 owls.


We can see that the data value $8$ for the number of cups consumed by Alex is an outlier here.

$\underset{–}{\text{Calculation of Mean:}}$

Mean of number of cups including Alex's consumption is

$\frac{1+2+3+2+3+8}{6}=\frac{19}{6}=3.1\overline{6}$

Mean of number of cups excluding Alex's consumption is

$\frac{1+2+3+2+3}{5}=\frac{11}{5}=2.2$

Hence, if Alex's consumption is ignored, the mean of the number of cups consumed will decrease.

$\therefore \underset{–}{\text{Option (c.) is incorrect.}}$

$\underset{–}{\text{Calculation of Median:}}$

The given ordered data set is


Median of the number of cups including Alex's consumption is

$\frac{2+3}{2}=\frac{5}{2}=2.5$

​​​​​​​Median of the number of cups excluding Alex's consumption is $2$.

Hence, if Alex's consumption is ignored, the median of the number of cups consumed will decrease.

$\therefore \underset{–}{\text{Option (a.) is incorrect.}}$

​​​​​​​$\underset{–}{\text{Calculation of Mode:}}$

The given ordered data set is

​​​​​​​
Here, the numbers $2$ and $3$ occur twice, which is the maximum number of occurrence. ​​​​​​​

Modes of number of cups including Alex's consumption are $2\text{and}3$.

Modes of number of cups excluding Alex's consumption are also $2\text{and}3$.

Hence, if Alex's consumption is ignored, the mode of the number of cups consumed will remain the same.

$\therefore \underset{–}{\text{Option (b.) is CORRECT.}}$