(C) Given the relation $3 \bar{x} = 2 M = 60.$From this,we can find the values of mean $(\bar{x})$ and median $(M)$:$\bar{x} = \frac{60}{3} = 20$$M =

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(C) Given the relation $3 \bar{x} = 2 M = 60.$From this,we can find the values of mean $(\bar{x})$ and median $(M)$:$\bar{x} = \frac{60}{3} = 20$$M = \frac{60}{2} = 30$The empirical relationship between mean,median,and mode $(Z)$ is given by the formula:$Z = 3 M - 2 \bar{x}$Substituting the values of $M$ and $\bar{x}$ into the formula:$Z = 3(30) - 2(20)$$Z = 90 - 40$$Z = 50$

Class 10 Mathematics Statistics Mix Examples - Statistics

Medium

If $3 \bar{x} = 2 M = 60,$ then $Z = \dots$

A
$0$
B
$40$
C
$50$
D
$60$

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Mix Examples - Statistics

If $Z - M = 4$,then $M - \bar{x} = \dots$

Medium

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Calculate the mean of the scores of $20$ students in a mathematics test:

Marks $10-20$ $20-30$ $30-40$ $40-50$ $50-60$

Number of students $2$ $4$ $7$ $6$ $1$

Medium

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For the following distribution:

Class $0-5$ $5-10$ $10-15$ $15-20$ $20-25$

Frequency $10$ $15$ $12$ $20$ $9$

the sum of the lower limits of the median class and the modal class is:

Medium

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The mean of the following frequency distribution is $43.75$. Find the missing frequency $f$.
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$
Frequency $8$ $4$ $20$ $45$ $64$ $32$ $f$ $8$ $2$ $2$

Medium

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The percentage of marks obtained by $100$ students in an examination are given below:

Marks $30-35$ $35-40$ $40-45$ $45-50$ $50-55$ $55-60$ $60-65$

Frequency $14$ $16$ $18$ $23$ $18$ $8$ $3$

Determine the median percentage of marks.

Medium

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Marks	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Number of students	$2$	$4$	$7$	$6$	$1$

Class	$0-5$	$5-10$	$10-15$	$15-20$	$20-25$
Frequency	$10$	$15$	$12$	$20$	$9$

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
Frequency	$8$	$4$	$20$	$45$	$64$	$32$	$f$	$8$	$2$	$2$

Marks	$30-35$	$35-40$	$40-45$	$45-50$	$50-55$	$55-60$	$60-65$
Frequency	$14$	$16$	$18$	$23$	$18$	$8$	$3$

If $3 \bar{x} = 2 M = 60,$ then $Z = \dots$

Similar Questions

If $Z - M = 4$,then $M - \bar{x} = \dots$

Calculate the mean of the scores of $20$ students in a mathematics test: Marks $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ Number of students $2$ $4$ $7$ $6$ $1$

For the following distribution: Class $0-5$ $5-10$ $10-15$ $15-20$ $20-25$ Frequency $10$ $15$ $12$ $20$ $9$ the sum of the lower limits of the median class and the modal class is:

The mean of the following frequency distribution is $43.75$. Find the missing frequency $f$.Class$0-10$$10-20$$20-30$$30-40$$40-50$$50-60$$60-70$$70-80$$80-90$$90-100$Frequency$8$$4$$20$$45$$64$$32$$f$$8$$2$$2$

The percentage of marks obtained by $100$ students in an examination are given below: Marks $30-35$ $35-40$ $40-45$ $45-50$ $50-55$ $55-60$ $60-65$ Frequency $14$ $16$ $18$ $23$ $18$ $8$ $3$ Determine the median percentage of marks.

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Calculate the mean of the scores of $20$ students in a mathematics test:

Marks $10-20$ $20-30$ $30-40$ $40-50$ $50-60$

Number of students $2$ $4$ $7$ $6$ $1$

For the following distribution:

Class $0-5$ $5-10$ $10-15$ $15-20$ $20-25$

Frequency $10$ $15$ $12$ $20$ $9$

the sum of the lower limits of the median class and the modal class is:

The mean of the following frequency distribution is $43.75$. Find the missing frequency $f$.
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$
Frequency $8$ $4$ $20$ $45$ $64$ $32$ $f$ $8$ $2$ $2$

The percentage of marks obtained by $100$ students in an examination are given below:

Marks $30-35$ $35-40$ $40-45$ $45-50$ $50-55$ $55-60$ $60-65$

Frequency $14$ $16$ $18$ $23$ $18$ $8$ $3$

Determine the median percentage of marks.