The total marks obtained by $40$ students in the Annual examination are given below
Marks $150 - 200$ $200 - 250$ $250 - 300$ $300 - 350$ $350 - 400$ $400 - 450$ $450 - 500$
Students $2$ $3$ $12$ $10$ $4$ $6$ $3$
Using step deviation method, find the mean of the above data.

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Solution

Marks

Midpoint( $x_{i}$ )

Students( $f_{i}$ )

Deviation( $d_{i}$ )

$u_{i}$

$u_{i} f_{i}$

150-200

175

2

-150

-3

-6

200-250

225

3

-100

-2

-6

250-300

275

12

-50

-1

-12

300-350

325

10

0

0

0

350-400

375

4

50

1

4

400-450

425

6

100

2

12

450-500

475

3

150

3

9

N= $\sum f_{i} = 40$ , h= $50$
A= $325$ , $d_{i} = x_{i} - A$ , $u_{i} = \frac{d_{i}}{h}$
Mean marks= $A + h (\frac{\sum u_{i} f_{i}}{N}) = 325 + 50 (\frac{1}{40})$
Mean marks= $326.25$

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\frac{\sum f_{i} u_{i}}{\sum f_{i}}

\begin{matrix} Class interval & Frequency (f_{i}) & Class mark (x_{i}) & d_{i} = x_{i} - a & u_{i} = \frac{d_{i}}{h} 0 - 100 & 40 & 50 & - 200 & - 2 100 - 200 & 39 & 150 & - 100 & - 1 200 - 300 & 34 & 250 & 0 & 0 300 - 400 & 30 & 350 & 100 & 1 400 - 500 & 45 & 450 & 200 & 2 \end{matrix}

Pocket money (in $R s$ )	$150 - 200$	$200 - 250$	$250 - 300$	$300 - 350$	$350 - 400$
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Marks	$150 - 200$	$200 - 250$	$250 - 300$	$300 - 350$	$350 - 400$	$400 - 450$	$450 - 500$
Students	$2$	$3$	$12$	$10$	$4$	$6$	$3$