4. Below is given frequency distribution of marks (out of 100) obtained by the students.
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
| No. of students | 3 | 5 | 7 | 10 | 12 | 15 | 12 | 6 | 2 | 8 |
Calculate mean marks scored by a student by 'Assumed mean method'.
Solution:
Class width ($h$) = 10, Assumed Mean ($A$) = 55
Marks Class Mark ($x_i$) $d_i = x_i - A$ No. of students ($f_i$) $f_i d_i$ 0 - 10 5 $- 50$ 3 $- 150$ 10 - 20 15 $- 40$ 5 $- 200$ 20 - 30 25 $- 30$ 7 $- 210$ 30 - 40 35 $- 20$ 10 $- 200$ 40 - 50 45 $- 10$ 12 $- 120$ 50 - 60 55 $\rightarrow$ A 0 15 0 60 - 70 65 10 12 120 70 - 80 75 20 6 120 80 - 90 85 30 2 60 90 - 100 95 40 8 320 Total $\sum f_i = 80$ $\sum f_i d_i = - 260$ $$ \bar{d} = \frac{\sum f_i d_i}{\sum f_i} $$ $$ \bar{d} = \frac{-260}{80} $$ $$ \bar{d} = -3.25 $$
$$ \text{Mean } (\bar{x}) = A + \bar{d} $$ $$ \text{Mean } (\bar{x}) = 55 + (-3.25) $$ $$ \text{Mean } (\bar{x}) = 55 - 3.25 $$ $$ \text{Mean } (\bar{x}) = 51.75 $$