Z - M = ldots ldots ldots times (M - bar{x}) | vedclass

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Question

(D) The empirical relationship between Mean $(\bar{x})$,Median $(M)$,and Mode $(Z)$ is given by the formula: $Z = 3M - 2\bar{x}$.
To find the value o

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(D) The empirical relationship between Mean $(\bar{x})$,Median $(M)$,and Mode $(Z)$ is given by the formula: $Z = 3M - 2\bar{x}$.
To find the value of the missing term in $Z - M = \ldots 	imes (M - \bar{x})$,we rearrange the formula:
$Z = 3M - 2\bar{x}$
Subtract $M$ from both sides:
$Z - M = 3M - 2\bar{x} - M$
$Z - M = 2M - 2\bar{x}$
Factor out $2$:
$Z - M = 2(M - \bar{x})$
Comparing this with the given expression,the missing value is $2$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$7$	$12$	$x$	$28$	$y$	$9$

Income (in $Rs.$)	Number of families
$0-5000$	$8$
$5000-10000$	$26$
$10000-15000$	$41$
$15000-20000$	$16$
$20000-25000$	$3$
$25000-30000$	$3$
$30000-35000$	$2$
$35000-40000$	$1$

$Z - M = \ldots \ldots \ldots \times (M - \bar{x})$

Similar Questions

In the formula $M = l + \frac{(\frac{n}{2} - cf)}{f} \times h$ for the median,$f = \ldots \ldots \ldots$

The mode of the following data is $33 \frac{1}{3}$ and the total frequency is $100$. Find the missing frequencies $x$ and $y$.

Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$

Frequency $7$ $12$ $x$ $28$ $y$ $9$

The mean of the first ten natural numbers is ........

In the formula $\bar{x} = A + \frac{\Sigma f_{i} u_{i}}{\Sigma f_{i}} \times c$,$c$ represents .......

The monthly income of $100$ families is given as follows:

Income (in $Rs.$) Number of families

$0-5000$ $8$

$5000-10000$ $26$

$10000-15000$ $41$

$15000-20000$ $16$

$20000-25000$ $3$

$25000-30000$ $3$

$30000-35000$ $2$

$35000-40000$ $1$

Calculate the modal income (in $Rs.$).

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