The following distribution shows the number of out door patients in 64 hospitals as follows. If the mean is 18, find the missing frequencies f₁ and f₂:
Number of patients
11-13
13-15
15-17
17-19
19-21
21-23
23-25
Number of hospitals
7
6
f₁
13
f₂
5
4
Answers
Dear student,
Answer: f1 = 9 , f2 = 20
Solution:
According to question total observation are 64.
So, summation of all frequencies would be 64.
∑ 7 +6 +f₁ +13 +f₂ +5 +4 = 35+f1+f2
35 + f1 + f2 = 64
f1 + f2 = 64-35
f1 + f2 = 29 --------------eq1
Mean = 18
18 = a + (∑( fi ui)/∑ fi )×h
From attached figure you get that a = 18 and h = 2
18 = 18 + (-11-f1+f2 )/( 35+f1+f2 )× 2
(18 -18 )÷2 = (-11-f1+f2 )/( 35+f1+f2 )
0 =(-11-f1+f2 )/( 35+f1+f2
-11 -f1 + f2 =0
-f1 +f2 = 11 --------------eq2
add eq 1 and eq2
2f2 = 11+29
f2 = 40/2
f2 = 20
put value of f2 in any one of eq1 and eq2
f1+f2 = 29
f1 = 29-f2
f1 = 29-20
f1 = 9
Hope it helps you.
TABLE IS IN THE ATTACHMENT..
STEP DEVIATION METHOD:
Step deviation method is used in the cases where the deviation from the assumed mean multiples of a common number. If the values of di for each class is a multiple of h the calculation become simpler by taking ui= di/h = (xi - A )/h
Here, h is the class size of each class interval.
Mean = A +( Σfiui/Σfi) × h
SOLUTION :
Given :
n = Σfi = 64 , h = 2
Let A = 16 (from the table)
n = Σfi = 64
35 + f1 + f2 = 64
f1 + f2 = 64 - 35 = 29
f1 + f2 = 29………..(1)
Mean = A +( Σfiui/Σfi) × h
[ By Step deviation method]
18 = 16 + (24 + 2f2 /64)× 2
18 - 16 + (24 + 2f2) / 32
2 ×32 = (24 + 2f2)
64 = 24 + 2f2
64 - 24 + 2f2
40 = 2f2
f2 = 40/2 = 20
f2 = 20
f1 + f2 = 29 [ from eq 1]
f1 + 20 = 29
f1 = 29 - 20 = 9
f1 = 9
Hence, the missing frequencies are f1 = 9 and f2 = 20
HOPE THIS ANSWER WILL HELP YOU...
