Name: Mean of Grouped Data: Example
Uploaded: 2019-07-19
Duration: 5 min 16 s
Description: Want to find out how to calculate the mean of grouped data when the class intervals are different? Watch this interesting video and learn more!

Question

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

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

Accepted Answer

$x_{i}$ $f_{i}$ $f_{i} x_{i}$

$10$ $17$ $170$

$f_{1}$ $f_{1}$ $f_{2}$

$Total 120$ $32$ $1600$

$70$ $f_{2}$ $70 f_{2}$

$90$ $19$ $1710$

$\sum f_{i} = 68 + f_{1} + f_{2} = 120$ $\sum f_{i} x_{i} = 3480 + 30 f_{1} + 70 f_{2}$

Given that the mean is $50 .$

$68 + f_{1} + f_{2} = 120$

$\Rightarrow f_{1} + f_{2} = 120 - 68$

$\Rightarrow f_{1} + f_{2} = 52 . . . . . . . (i)$

The mean $\bar{X}$ $= \frac{\sum f_{i} x_{i}}{N}$

$\frac{3480 + 30 f_{1} + 70 f_{2}}{68 + f_{1} + f_{2}} = 50$

$\Rightarrow 50 (68 + f_{1} + f_{2}) = 3480 + 30 f_{1} + 70 f_{2}$

$\Rightarrow 3400 + 50 f_{1} + 50 f_{2} = 3480 + 30 f_{1} + 70 f_{2}$

$\Rightarrow 50 f_{1} + 50 f_{2} - 30 f_{1} - 70 f_{2} = 3480 - 3400$

$\Rightarrow 20 f_{1} - 20 f_{2} = 80$

$\Rightarrow 20 (f_{1} - f_{2}) = 80$

$\Rightarrow f_{1} - f_{2} = \frac{80}{20}$

$\Rightarrow f_{1} - f_{2} = 4 . . . . . . . . . (ii)$

Adding $(i)$ and $(i i)$ , we get

$(f_{1} + f_{2}) + (f_{1} - f_{2}) = 52 + 4$

$\Rightarrow f_{1} + f_{2} + f_{1} - f_{2} = 56$

$\Rightarrow 2 f_{1} = 56$

$\Rightarrow f_{1} = \frac{56}{2}$

$\Rightarrow f_{1} = 28$

Putting the value of $f_{1}$ in the second equation, we get

$28 - f_{2} = 4$

$\Rightarrow 4 = 28 - f_{2}$

$\Rightarrow f_{2} = 28 - 4$

$\Rightarrow f_{2} = 24$

Hence, the values of $f_{1}$ and $f_{2}$ are $28$ and $24$ respectively.

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

$x$ $10$ $30$ $50$ $70$ $90$

$y$ $17$ $f_{1}$ $32$ $f_{2}$ $19$ $Total 120$

Important Questions on Measures of Central Tendency

Learn and Prepare for any exam you want !

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 y 17 f1 32 f2 19 Total 120

Important Questions on Measures of Central Tendency

Learn and Prepare for any exam you want !

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

$x$ $10$ $30$ $50$ $70$ $90$

$y$ $17$ $f_{1}$ $32$ $f_{2}$ $19$ $Total 120$