Question

The following are the marks obtained in Science by students in class X.
The mean was calculated to be 63.33.
Is this mean an appropriate representation of the average marks obtained?
If no, what would be the most appropriate measure of central tendency for the correct representation of the marks distribution?
What is the value of this measure of central tendency for the given data?

$\begin{array}{cc}\text{Marks}& \text{Frequency}\\ 10-20& 1\\ 20-30& 0\\ 30-40& 0\\ 40-50& 0\\ 50-60& 1\\ 60-70& 5\\ 70-80& 15\\ 80-90& 20\\ 90-100& 3\end{array}$

Answer 1

Most of the class got marks above 70.
However, since one student got marks below 20, the mean got lowered to 63.33, which is a poor representation of the performance by the rest of the class.
A better representation would be the median, which would be the typical value.
The median can be calculated as follows:
$\begin{array}{ccc}\text{Marks}& \text{Frequency}& \text{Cumulative frequency}\\ 10-20& 1& 1\\ 20-30& 0& 1\\ 30-40& 0& 1\\ 40-50& 0& 1\\ 50-60& 1& 2\\ 60-70& 5& 7\\ 70-80& 15& 22\\ 80-90& 20& 42\\ 90-100& 3& 45\end{array}$
Here n = 45 and $\frac{n}{2}=22.5$. Hence, the median class is 80-90.
$\therefore$, median = l + $\frac{\frac{n}{2}-cf}{f}\times h=80+\frac{22.5-22}{42}\times 10=80.12$