Krishna
0

Step 1: Recall the formula of the mean of the grouped data

NOTE: The mean (or average) of observations is the sum of the values of

all the observations divided by the total number of observations.

Let x_1, x_2, x_3............, x_n be observations with respective

frequencies f_1, f_2,............f_n

Mean = \frac{f_1x_1 + f_2x_2 + ........f_nx_n}{f_1 + f_2 +..........+ f_n}

or

Mean = \frac{\Sigma f_ix_i}{\Sigma f_i}

GIVEN:  The pocket allowance mean = 18

Find the missing frequency = ?

Step 2: Re-organize given data in the table and find the sum of all observations.

Sum of the values of all the observations \Sigma f_ix_i=752\ +\ 20f

Total number of observations \Sigma f_i=44\ +\ f

So, the mean = \frac{752\ +\ 20f}{44\ +\ f}

Step 3: Find the missing frequency

Given Mean = 18

So,     18 = \frac{752 + 20f}{44 + f}

18 * (44 + f) = 752 + 20f

18f - 20f = 752 - 792

-2f = - 40

f = \frac{40}{2}

f = 20

Hence, the missing frequency f = 20