Calculate mean with step Deviation method from the following data.
Marks $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$
No. of student $4$ $6$ $10$ $20$ $10$

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Solution

Class inreval

Mid values $(x_{i})$

Frequency $(f_{i})$

$d_{i} = x_{i} - A$

$u_{i} = \frac{d_{i}}{h}$

$F_{i} u_{i}$

0-10

5

4

-20

-2

-8

10-20

15

6

-10

-1

-6

20-30

25=A

10

0

0

0

30-40

35

20

10

1

20

40-50

45

10

20

2

20

N=50

Total=26

$h = 10, A = 25, N = 50, \sum f_{i} u_{i} = 26$
Mean $(¯ ¯ ¯ x) = A + h [\frac{1}{N} \sum f_{i} u_{i}]$
put the values
$M e a n = 30.2$

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