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Find the mean from the following frequency distribution of marks at a test in statistics:
| Marks ($x$): | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| No. of students ($f$): | 15 | 50 | 80 | 76 | 72 | 45 | 39 | 9 | 8 | 6. |
Given:
The number of marks of students in a test in statistics.
To do:
We have to find the mean from the given frequency distribution of marks at a test in statistics.
Solution:
Let the assumed mean be $A=25$
| Marks ($x_i$) | No. of students ($f_i$) | $d_i = x_i - A$ $A = 25$ | $f_i \times\ d_i$ |
| 5 | 15 | $-20$ | $-300$ |
| 10 | 50 | $-15$ | $-750$ |
| 15 | 80 | $-10$ | $-800$ |
| 20 | 76 | $-5$ | $-380$ |
| 25-$A$ | 72 | 0 | 0 |
| 30 | 45 | 5 | 225 |
| 35 | 39 | 10 | 390 |
| 40 | 9 | 15 | 135 |
| 45 | 8 | 20 | 160 |
| 50 | 6 | 25 | 150 |
| Total | $\sum{f_i}=400$ | $\sum{f_id_i}=-1170$ |
We know that,
Mean $=A+\frac{\sum{f_id_i}}{\sum{f_i}}$
Therefore,
Mean $=25+\frac{-1170}{400}$
$=25-2.925$
$=22.075$
The average number of marks obtained per student is $22.075$.
Updated on: 10-Oct-2022
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