Question

16-Calculate Standard Deviation by Actual mean method from the given data: Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-50​

Answer 1

Answer:

X Mid Point (X) Frequency (F) i=class interval width A=45 Assumed mean u=

i

x−A

fu

0-10 5 3 10 45 -4 -12

10-20 15 5 10 45 -3 -15

20-30 25 6 10 45 -2 -12

30-40 35 7 10 45 -1 -7

40-50 45=A 8 10 45 0 0

50-60 55 9 10 45 1 9

60-70 65 10 10 45 2 20

70-80 75 12 10 45 3 36

80-90 85 6 10 45 4 24

90-100 95 4 10 45 5 20

Σf=70 Σfu=63

The formula used for arithmetic mean of grouped data by step deviation method is,

X

=A+

∑f

∑fu

×i

A= Assumed mean of the given data

∑ = Summation of the frequencies given in the grouped data

∑fu = Summation of the frequencies and deviation of a given mean data

u=

i

(x−A)

i= Class interval width

X

= arithmetic mean

X

=45+

70

63

×10

=45+9

=54