# 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 :

This is a grouped frequency distribution.

To find f1 and f2, we’ll need to find mean of the following distribution by direct method and equate it to the given mean of the following distribution, 18.

This given data is exclusive, grouped frequency distribution.

So, let’s construct a table finding midpoints and stating frequencies.

So now, we have

xifi = 608 + 16f1 + 20f2

And fi = 35 + f1 + f2

Mean is given by

[given, mean = 18 and using the values from the table]

18 × (35 + f1 + f2) = 608 + 16f1 + 20f2

630 + 18f1 + 18f2 = 608 + 16f1 + 20f2

20f2 – 18f2 + 16f1 – 18f1 = 630 – 608

2f2 – 2f1 = 22

2(f2 – f1) = 22

f2 – f1 = 11 …(i)

Since, there are 64 hospitals.

Number of hospitals = 64

Frequency = 64

fi = 64

35 + f1 + f2 = 64

f1 + f2 = 64 – 35

f1 + f2 = 29 …(ii)

Solving equations (i) and (ii), we get

f2 – f1 = 11

f2 + f1 = 29

2f2 + 0 = 40

2f2 = 40

f2 = 20

Putting f2 = 20 in equation (ii), we get

f1 + 20 = 29

f1 = 29 – 20

f1 = 9

Thus, the missing frequencies are f1 = 9 and f2 = 20.

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