The mean of the following frequency distribut | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) To find the mean of a grouped frequency distribution,we use the formula $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$.First,calculate the class marks

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(B) To find the mean of a grouped frequency distribution,we use the formula $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$.First,calculate the class marks $(x_i)$ for each interval:$0-20: x_1 = 10$$20-40: x_2 = 30$$40-60: x_3 = 50$$60-80: x_4 = 70$$80-100: x_5 = 90$$100-120: x_6 = 110$Now,calculate $\sum f_i x_i = (10 	imes 10) + (f 	imes 30) + (7 	imes 50) + (6 	imes 70) + (5 	imes 90) + (4 	imes 110) = 100 + 30f + 350 + 420 + 450 + 440 = 1760 + 30f$.Calculate $\sum f_i = 10 + f + 7 + 6 + 5 + 4 = 32 + f$.Given the mean $\bar{x} = 46$,we have $46 = \frac{1760 + 30f}{32 + f}$.$46(32 + f) = 1760 + 30f$$1472 + 46f = 1760 + 30f$$46f - 30f = 1760 - 1472$$16f = 288$$f = \frac{288}{16} = 18$.

Class	$0-20, 20-40, 40-60, 60-80, 80-100, 100-120$
Frequency	$10, f, 7, 6, 5, 4$

Class	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
Frequency	$5$	$x$	$20$	$y$	$2$

Income (in $Rs.$)	Number of families
$0-5000$	$8$
$5000-10000$	$26$
$10000-15000$	$41$
$15000-20000$	$16$
$20000-25000$	$3$
$25000-30000$	$3$
$30000-35000$	$2$
$35000-40000$	$1$

The mean of the following frequency distribution is $46$. Find the missing frequency $f$.

Class $0-20, 20-40, 40-60, 60-80, 80-100, 100-120$

Frequency $10, f, 7, 6, 5, 4$

Similar Questions

Cumulative frequency distribution is used to calculate the $\ldots \ldots \ldots$ of a frequency distribution.

Is it correct to say that an ogive is a graphical representation of a frequency distribution? Give reason.

.......... is not a measure of central tendency.

The median of the following frequency distribution is $50$ and the total frequency is $60$. Find the missing frequencies $x$ and $y$.

Class $0-20$ $20-40$ $40-60$ $60-80$ $80-100$

Frequency $5$ $x$ $20$ $y$ $2$

The monthly income of $100$ families is given as follows:

Income (in $Rs.$) Number of families

$0-5000$ $8$

$5000-10000$ $26$

$10000-15000$ $41$

$15000-20000$ $16$

$20000-25000$ $3$

$25000-30000$ $3$

$30000-35000$ $2$

$35000-40000$ $1$

Calculate the modal income (in $Rs.$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module

The mean of the following frequency distribution is $46$. Find the missing frequency $f$. Class $0-20, 20-40, 40-60, 60-80, 80-100, 100-120$ Frequency $10, f, 7, 6, 5, 4$