Question

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

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

Measure the central tendency of the above data.

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

Answer 1

The correct option is A

Mean = 87.25, Median = 84.5 and Mode = 82

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

We know that,
$\Rightarrow \text{Mean}=\frac{Sumofobservations}{Numberofobservations}$

Now,
$\Rightarrow \text{Mean}=\frac{87+82+82+98}{4}$
$\Rightarrow \text{Mean}=87.25$

Since, the number of observations is even, the median would be the average of the middle terms arranged in either ascending or descending order i.e. 82, 82, 87, 98.

$\text{Median}$ = $\frac{(\frac{n}{2}{)}^{th}\text{term}+{(\frac{n}{2}+1)}^{th}\text{term}}{2}$
= $\frac{2^{nd}term+3^{rd}term}{2}$
= $\frac{82+87}{2}$
= $84.5$

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

Thus, mean = 87.25, median = 84.5 and mode = 82.