Calculate Mean by Step Deviation Method
Solve problem 10 by 'Step Deviation Method'. Below is the 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 |
Solution:
Let the Assumed mean ($A$) be $45$.
Class width ($h$) = $10$
Class mark Class Mark ($x_i$) $d_i = x_i - A$ $u_i = \frac{d_i}{h}$ No. of students ($f_i$) $f_i u_i$ 0 - 10 5 -40 -4 3 -12 10 - 20 15 -30 -3 5 -15 20 - 30 25 -20 -2 7 -14 30 - 40 35 -10 -1 10 -10 40 - 50 45 $\rightarrow$ A 0 0 12 0 50 - 60 55 10 1 15 15 60 - 70 65 20 2 12 24 70 - 80 75 30 3 6 18 80 - 90 85 40 4 2 8 90 - 100 95 50 5 8 40 Total 80 54 Calculate $\bar{u}$:
$$ \bar{u} = \frac{\sum f_i u_i}{\sum f_i} $$
$$ \bar{u} = \frac{54}{80} $$
$$ \bar{u} = 0.675 $$Calculate the Mean ($\bar{x}$):
$$ \text{Mean } (\bar{x}) = A + h\bar{u} $$
$$ \text{Mean } (\bar{x}) = 45 + 10(0.675) $$
$$ \text{Mean } (\bar{x}) = 45 + 6.75 $$
$$ \text{Mean } (\bar{x}) = 51.75 $$