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 $2$.

Marks	Number of students
Below $10$	$3$
Below $20$	$12$
Below $30$	$27$
Below $40$	$57$
Below $50$	$75$
Below $60$	$80$

Class	$1-3$	$3-5$	$5-7$	$7-9$	$9-11$
Frequency	$6$	$3$	$8$	$2$	$1$

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
No. of students	$20$	$10$	$20$	$30$	$20$

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

Similar Questions

For the following distribution,the modal class is:

Marks Number of students

Below $10$ $3$

Below $20$ $12$

Below $30$ $27$

Below $40$ $57$

Below $50$ $75$

Below $60$ $80$

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

For the calculation of mode of the following frequency distribution,$f_{0} = \dots \dots \dots \dots \dots$

Class $1-3$ $3-5$ $5-7$ $7-9$ $9-11$

Frequency $6$ $3$ $8$ $2$ $1$

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

Calculate the mean of the frequency distribution of the marks scored by $100$ students in a mathematics test:

Marks $0-10$ $10-20$ $20-30$ $30-40$ $40-50$

No. of students $20$ $10$ $20$ $30$ $20$

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