Calculate the mean of the frequency distribut | vedclass

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(A) To calculate the mean,we use the formula $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$,where $x_i$ is the class mark.$1$. Find the class marks $(x_i)$

Vedclass · Accepted Answer

$27$

Vedclass · Answer

(A) To calculate the mean,we use the formula $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$,where $x_i$ is the class mark.$1$. Find the class marks $(x_i)$ for each interval:- For $0-10$,$x_1 = (0+10)/2 = 5$- For $10-20$,$x_2 = (10+20)/2 = 15$- For $20-30$,$x_3 = (20+30)/2 = 25$- For $30-40$,$x_4 = (30+40)/2 = 35$- For $40-50$,$x_5 = (40+50)/2 = 45$$2$. Calculate $f_i x_i$:- $20 	imes 5 = 100$- $10 	imes 15 = 150$- $20 	imes 25 = 500$- $30 	imes 35 = 1050$- $20 	imes 45 = 900$$3$. Calculate $\sum f_i x_i = 100 + 150 + 500 + 1050 + 900 = 2700$.$4$. Calculate $\sum f_i = 20 + 10 + 20 + 30 + 20 = 100$.$5$. Mean $\bar{x} = 2700 / 100 = 27$.

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

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$
Frequency	$4$	$7$	$x$	$18$	$15$	$8$	$7$

Class	$0-15$	$15-30$	$30-45$	$45-60$	$60-75$	$75-90$	$90-105$
Frequency	$4$	$5$	$23$	$45$	$66$	$42$	$15$

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 $20$ $10$ $20$ $30$ $20$

Similar Questions

The median class of the following frequency distribution is ...........
Class $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$
Frequency $6$ $10$ $5$ $6$ $4$ $2$ $2$

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

The mode of the following frequency distribution is $37$. Find the missing frequency $x$.
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$
Frequency $4$ $7$ $x$ $18$ $15$ $8$ $7$

In the usual notations,$Z - M = \ldots \ldots \ldots \quad (M - \bar{x})$

Find the mode of the following frequency distribution:

Class $0-15$ $15-30$ $30-45$ $45-60$ $60-75$ $75-90$ $90-105$

Frequency $4$ $5$ $23$ $45$ $66$ $42$ $15$

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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 $20$ $10$ $20$ $30$ $20$