(A) Let the number of individuals in the two groups be $n_1$ and $n_2$ respectively.Given: $\bar{x}_1 = 400$,$\bar{x}_2 = 480$,and the combined mean $

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(A) Let the number of individuals in the two groups be $n_1$ and $n_2$ respectively.Given: $\bar{x}_1 = 400$,$\bar{x}_2 = 480$,and the combined mean $\bar{x} = 430$.The formula for the combined mean is $\bar{x} = \frac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1 + n_2}$.Substituting the values: $430 = \frac{400n_1 + 480n_2}{n_1 + n_2}$.$430(n_1 + n_2) = 400n_1 + 480n_2$.$430n_1 + 430n_2 = 400n_1 + 480n_2$.$430n_1 - 400n_1 = 480n_2 - 430n_2$.$30n_1 = 50n_2$.$\frac{n_1}{n_2} = \frac{50}{30} = \frac{5}{3}$.

Class 11 Mathematics Statistics Word problem -Statistics

Medium

The mean income of a group of individuals is $400$ and the mean income of another group of individuals is $480$. If the mean income of all the individuals in both groups combined is $430$,find the ratio of the number of individuals in the two groups.

A
$5/3$
B
$2/3$
C
$1/2$
D
$5/4$

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Class	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
$f$	$17$	$f_1$	$32$	$f_2$	$19$

Items of expenditure	Number of families
$Education$	$150$
$Food and clothing$	$400$
$House rent$	$40$
$Electricity$	$250$
$Miscellaneous$	$160$

The mean income of a group of individuals is $400$ and the mean income of another group of individuals is $480$. If the mean income of all the individuals in both groups combined is $430$,find the ratio of the number of individuals in the two groups.

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The mean of the following frequency distribution is $50$ and $\Sigma f = 120$. Find the missing frequencies $f_1$ and $f_2$.
Class $0-20$ $20-40$ $40-60$ $60-80$ $80-100$
$f$ $17$ $f_1$ $32$ $f_2$ $19$

$A$ pie chart is to be drawn for representing the following data. The value of the central angle for food and clothing would be...$^o$

Items of expenditure Number of families

$Education$ $150$

$Food and clothing$ $400$

$House rent$ $40$

$Electricity$ $250$

$Miscellaneous$ $160$