Question

Michael appeared in an examination and obtained the following marks out of 100

$$\begin{array}{cc}\text{Subject}& \text{Marks}\\ \text{Physics}& 87\\ \text{Chemistry}& 82\\ \text{Biology}& 82\\ \text{Mathematics}& 98\end{array}$$

Find the measures of central tendency for the above data.

• A. Mean = 87.25, Median = 84.5, Mode = 82
• B. Mean = 86.25, Median = 82, Mode = 98
• C. Mean = 87.25, Median = 81, Mode= 87
• D. Mean= 87.25, Median = 87, Mode = 82

Answer 1

The correct option is A

Mean = 87.25, Median = 84.5, Mode = 82

The Central tendency has three measures namely mean, median and mode.

$\text{Mean}=\frac{Sumofobservations}{Totalnumberofobservations}$.

$\text{Mean}=\frac{87+82+82+98}{4}=87.25$.
Since the number of observations is even, the median would be the average of the middle terms arranged in either ascending or descending order.
$\text{Median}$
= $\frac{(\frac{n}{2}{)}^{th}\text{term}+{(\frac{n}{2}+1)}^{th}\text{term}}{2}$
= $\frac{87+82}{2}$
= $84.5$

The mode is the most frequently occurring value in the observation table, which is equal to 82.