Question

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

Answer 1

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.

Answer 2

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...