I find the mean for the following distribution-
5.
15
8
25
20
35
10
45
5
f
Answers
Answer:
X Mid point (x) Frequency (F) i=class interval width A=22.5 Assumed mean d'=
i
x−A
fd'
0-5 2.5 3 5 22.5 -4 -12
5-10 7.5 5 5 22.5 -3 -15
10 -15 12.5 7 5 22.5 -2 -14
15-20 17.5 8 5 22.5 -1 -8
20-25 22.5=A 10 5 22.5 0 0
25-30 27.5 11 5 22.5 1 11
30-35 32.5 14 5 22.5 2 28
35-40 37.5 19 5 22.
5 3 57
40-45 42.5 15 5 22.5 4 60
45-50 47.5 13 5 22.5 5 65
Σf=105 Σfd
′
=172
The formula used for arithmetic mean of grouped data by step deviation method is,
X
=A+
∑f
∑fd
′
×i
A= Assumed mean of the given data
∑ = Summation of the frequencies given in the grouped data
∑fd
′
= Summation of the frequencies and deviation of a given mean data
d
′
=
i
(x−A)
i= Class interval width
X
= arithmetic mean
X
=22.5+
105
172
×5
=22.5+8.19
=30.69 ≈ 31