Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.

x: 10 30 50 70 90

f: 17 f₁ 32 f₂ 19

Total 120.

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Solution

The given distribution in tabulated form is

We have to find the value of missing frequencies f₁ and f₂, using the information that the mean of the distribution is 50 and the total frequency is 120.

Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing.

Find the sum of all entries in the second and third column to obtain N and respectively. Therefore,

The mean is

Hence, we have two equations

Adding them we get

Putting the value of f₁ in the second equation we get

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Similar questions

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is $50$ .

$\begin{matrix} x_{i} & f_{i} 10 & 17 30 & f_{1} 50 & 32 70 & f_{2} 90 & 19 Total & 120 \end{matrix}$

Q. Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is

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$x$ :	$10$	$30$	$50$	$70$	$90$
$f$ :	$17$	$f_{1}$	$32$	$f_{2}$	$19$	Total: $120$

Q. Find the missing frequencies in the following frequency distribution whose mean is

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and total frequency is

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Find the missing frequencies in the following distribution , if the sum of the frequencies is $120$ and the mean is $50$ .

$\begin{matrix} Class & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 Frequency & 17 & f_{1} & 32 & f_{2} & 19 \end{matrix}$

Find the missing frequencies in the following frequency distribution whose mean is 50.
$\begin{matrix} x & 10 & 30 & 50 & 70 & 90 & Total f & 17 & f_{1} & 32 & f_{2} & 19 & 120 \end{matrix}$

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Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50. x: 10 30 50 70 90 f: 17 f1 32 f2 19 Total 120.

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.

x: 10 30 50 70 90

f: 17 f₁ 32 f₂ 19

Total 120.