If Z=12 and M=16, then bar{x}= ............ | vedclass

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Question

(C) The empirical relationship between Mean $(\bar{x})$,Median $(M)$,and Mode $(Z)$ is given by the formula:
$Z = 3M - 2\bar{x}$
Given values are $Z

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(C) The empirical relationship between Mean $(\bar{x})$,Median $(M)$,and Mode $(Z)$ is given by the formula:
$Z = 3M - 2\bar{x}$
Given values are $Z = 12$ and $M = 16$.
Substituting these values into the formula:
$12 = 3(16) - 2\bar{x}$
$12 = 48 - 2\bar{x}$
Rearranging the equation to solve for $\bar{x}$:
$2\bar{x} = 48 - 12$
$2\bar{x} = 36$
$\bar{x} = \frac{36}{2}$
$\bar{x} = 18$

Class interval	$10-25$	$25-40$	$40-55$	$55-70$	$70-85$	$85-100$
Number of students	$2$	$3$	$7$	$6$	$6$	$6$

Class	$0-30$	$30-60$	$60-90$	$90-120$	$120-150$	$150-180$
Frequency	$8$	$15$	$16$	$20$	$12$	$9$

If $Z=12$ and $M=16,$ then $\bar{x}=$ ............

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