The marks obtained out of 50, by 102 students in a Physics test are given in the frequency table below:
Question:
The marks obtained out of 50, by 102 students in a Physics test are given in the frequency table below:
Find the average number of marks.
Solution:
Let the assume mean be $A=25$.
We know that mean, $\bar{X}=A+\frac{1}{N} \sum_{i=1}^{n} f_{i} d_{i}$
Now, we have $N=\sum f_{i}=102, \sum f_{i} d_{i}=110$ and $A=25$.
Putting the values in the above formula, we get
$\bar{X}=A+\frac{1}{N} \sum_{i=1}^{n} f_{i} d_{i}$
$=25+\frac{1}{102} \times(110)$
$=25+\frac{110}{102}$
$=25+1.078$
$=26.078$
$\approx 26.08($ approximate $)$
Hence, the average number of marks is 26.08.