The marks obtained out of 50, by 102 students in a physics test are given in the frequency table below:
| Marks ($x$): | 15 | 20 | 22 | 24 | 25 | 30 | 33 | 38 | 45 |
| Frequency ($f$): | 5 | 8 | 11 | 20 | 23 | 18 | 13 | 3 | 1 |
Find the average number of marks.
Given:
The marks obtained out of 50, by 102 students in a physics test are given in the frequency table.
To do:
We have to find the average number of marks.
Solution:
Let the assumed mean be $A=25$
| Marks ($x$) | Frequency ($f$) | $d_i = x_i -A$ $A=25$ | $f_i \times\ d_i$ |
| 15 | 5 | $-10$ | $-50$ |
| 20 | 8 | $-5$ | $-40$ |
| 22 | 11 | $-3$ | $-33$ |
| 24 | 20 | $-1$ | $-20$ |
| 25 - $A$ | 23 | 0 | 0 |
| 30 | 18 | 5 | 90 |
| 33 | 13 | 8 | 104 |
| 38 | 3 | 13 | 39 |
| 45 | 1 | 20 | 20 |
| Total | $\sum{f_i}=102$
| | $\sum{f_id_i}=110$
|
 We know that,
Mean $=A+\frac{\sum{f_id_i}}{\sum{f_i}}$  
Therefore,
Mean $=25+\frac{110}{102}$
$=25+1.08$
$=26.08$
The average number of marks is $26.08$.
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