Question

Compute the mean of the following frequency distribution using step deviation method. :
Class 0-11 11-22 22-33 33-44 44-55 55-66 Frequency 9 17 28 26 15 8

Answer 1

Step-by-step explanation:

Answer:-

Class interval width (i) = 10

Converting the given data into frequency distribution table

Class interval X No. of employees

F d=

i

X−A

Fd

11-21 16 2 -2 -4

21-31 26 4 -1 -4

31-41 36=A 6 0 0

41-51 46 8 1 8

51-61 56 10 2 20

Σf=30 Σfd=20

Mean = A+

Σf

Σfd

=36+

30

20

×10=36+6.66=42.66

C) 42.66

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Answer 2

Given: Class : 0-11 11-22 22-33 33-44 44-55 55-66

            Frequency: 9 17 28 26 15 8

To find: The mean of the following distribution by step deviation method.

Solution:

The formula of the mean using the step deviation method is:

$Mean=A+\frac{Sum-of-fd}{N} *i$

where, A is the assumed mean, N is the sum of frequency and i is the class interval.

Now,

Class        Frequency(f)      Mid Value       d=(x-A)/i            fd

0-11                 9                     5.5                 -2                    -18

11-22              17                    16.5                 -1                     -17

22-33            28                    27.5                0                      0

33-44            26                     38.5                1                      26

44-55            15                      49.5                2                     30

55-66             8                      60.5                3                     24

The assumed mean is $=27.5$

Sum of ∑fd $=45$

Sum of the frequency ∑f $=103$

i = 11 (which is the class difference)

The mean $=A+\frac{Sum-of-fd}{N}*i$

$=27.5+\frac{45}{103}*11$

$=27.5+4.80$

$=32.30$

Final answer:

The mean of the following distribution is 32.30.