If Z+M=34 and M+bar{x}=40, then M=ldots ldots | vedclass

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Question

(C) We know the empirical relationship between Mean $(\bar{x})$,Median $(M)$,and Mode $(Z)$ is given by: $Z = 3M - 2\bar{x}$.
Given equations:
$1) Z

Vedclass · Accepted Answer

$19$

Vedclass · Answer

(C) We know the empirical relationship between Mean $(\bar{x})$,Median $(M)$,and Mode $(Z)$ is given by: $Z = 3M - 2\bar{x}$.
Given equations:
$1) Z + M = 34 \implies Z = 34 - M$
$2) M + \bar{x} = 40 \implies \bar{x} = 40 - M$
Substitute these into the empirical formula:
$34 - M = 3M - 2(40 - M)$
$34 - M = 3M - 80 + 2M$
$34 - M = 5M - 80$
$34 + 80 = 5M + M$
$114 = 6M$
$M = \frac{114}{6} = 19$
Therefore,the value of $M$ is $19$.

Height (in $cm$)	Number of students
$150-155$	$15$
$155-160$	$13$
$160-165$	$10$
$165-170$	$8$
$170-175$	$9$
$175-180$	$5$

If $Z+M=34$ and $M+\bar{x}=40,$ then $M=\ldots \ldots \ldots . . .$

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