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# 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.