The mean of the following distribution is 48 and sum of all the frequencies is 50. Find the missing frequencies x and y.

The mean of the following distribution is 48 and sum of all the frequencies is 50. Find the missing frequencies x and y.

1. A
15 and 10
2. B
10 and 15
3. C
13 and 12
4. D
12 and 13

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Solution:

Given that the mean of the following distribution is 48 and sum of all the frequencies is 50.
We know that the frequency is generally the total sum of all the data divided by the total number of data present in the following table.
And mean is the measure of central tendency as it indicates the average value of the data.
Find the value of x and y.
$\sum _{}^{}{f}_{i}=25+x+y=50$.
$⇒x=25-13$
$⇒x=12$
Substitute the value of x into the equation.
$\mathit{Mean}=a+\left(\frac{\sum _{}^{}{f}_{i}{u}_{i}}{\sum _{}^{}{f}_{i}}\right)×h$
In the formula, a is the  assumed mean, is the frequency of class, is the deviation of class, ${x}_{i}$ = class mark = , ${u}_{i}=\frac{{x}_{i}-a}{h}$  , Total number of observations.

$⇒15=2y-11$
$⇒y=13$
Considering the calculated values above,  the value of x and y is 12 and 13 respectively.
Hence, option 4 is correct.

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