If bar{x} = Z - 3 and M = 22,then the mean is | vedclass

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

Vedclass · Accepted Answer

$21$

Vedclass · Answer

(B) The empirical relationship between Mean $( \bar{x})$,Median $(M)$,and Mode $(Z)$ is given by the formula: $Z = 3M - 2\bar{x}$.
Given that $\bar{x} = Z - 3$,we can express the mode as $Z = \bar{x} + 3$.
Substituting these values into the empirical formula:
$\bar{x} + 3 = 3(22) - 2\bar{x}$
$\bar{x} + 3 = 66 - 2\bar{x}$
Adding $2\bar{x}$ to both sides:
$3\bar{x} + 3 = 66$
Subtracting $3$ from both sides:
$3\bar{x} = 63$
Dividing by $3$:
$\bar{x} = 21$.
Therefore,the mean is $21$.

Height (in $cm$)	Frequency	Cumulative frequency
$150-155$	$12$	$a$
$155-160$	$b$	$25$
$160-165$	$10$	$c$
$165-170$	$d$	$43$
$170-175$	$e$	$48$
$175-180$	$2$	$f$
Total	$50$	-

Class	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$
Frequency	$8$	$12$	$27$	$x$	$55$	$37$	$y$

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

Class	$1-3$	$3-5$	$5-7$	$7-10$
Frequency	$9$	$22$	$27$	$17$

If $\bar{x} = Z - 3$ and $M = 22$,then the mean is ..........

Similar Questions

Find the unknown entries $a, b, c, d, e, f$ in the following distribution of heights of students in a class:

Height (in $cm$) Frequency Cumulative frequency

$150-155$ $12$ $a$

$155-160$ $b$ $25$

$160-165$ $10$ $c$

$165-170$ $d$ $43$

$170-175$ $e$ $48$

$175-180$ $2$ $f$

Total $50$ -

The mode of the following frequency distribution is $64$ and the total frequency is $200.$ Find the missing frequencies $x$ and $y.$

Class $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$

Frequency $8$ $12$ $27$ $x$ $55$ $37$ $y$

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

Find the mean of the distribution:

Class $1-3$ $3-5$ $5-7$ $7-10$

Frequency $9$ $22$ $27$ $17$

For the calculations of mode of a grouped data,the maximum frequency of a class is denoted by $\ldots \ldots \ldots . .$

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