The
following table gives frequency distribution of trees planted by different
Housing Societies in a particular locality:
|
No. of Trees
|
No. of Housing Societies
|
|
10 – 15
|
2
|
|
15 – 20
|
7
|
|
20 – 25
|
9
|
|
25 – 30
|
8
|
|
30 – 35
|
6
|
|
35 – 40
|
4
|
Find
the mean number of trees planted by Housing Societies by using 'Assumed Mean Method'.
Solution:
|
No.
of Trees
|
Class
Mark
(xi)
|
xi
– A = xi – 22.5
(di)
|
No.
of Housing
Societies
(fi)
|
fidi
|
|
10 – 15
|
12.5
|
-10
|
2
|
-20
|
|
15 – 20
|
17.5
|
-5
|
7
|
-35
|
|
20 – 25
|
22.5 → A
|
0
|
9
|
0
|
|
25 – 30
|
27.5
|
5
|
8
|
40
|
|
30 – 35
|
32.5
|
10
|
6
|
60
|
|
35 – 40
|
37.5
|
15
|
4
|
60
|
|
Total
|
-
|
-
|
Σfi =
36
|
Σfidi
= 105
|
|
|
|
|
|
|
|
|
|
|
|
|
|
d̅
|
=
|
Σ fidi
|
=
|
105
|
|
|
|
Σfi
|
|
36
|
|
|
|
|
|
|
|
∴
d̅
|
=
|
2.917
|
|
|
|
|
|
|
|
|
|
∴
x̅
|
=
|
A + d̅
|
|
|
|
|
|
|
|
|
|
∴ x̅
|
=
|
22.5 + 2.917
|
|
|
|
|
|
|
|
|
|
∴ x̅
|
=
|
25.417
|
|
|
|
|
|
|
|
|
|
∴ x̅
|
=
|
25.42 trees.
|
|
|
