Mathematics>Statistics and Probability>Measures of Central Tendency>Mean of Grouped Data

Mean of Grouped Data

IMPORTANT

Mean of Grouped Data: Overview

In this topic, we will learn about arithmetic mean of grouped data or a discrete frequency distribution. In a discrete frequency distribution, arithmetic mean may be computed using Direct method, Short-cut method, and Step-deviation method.

Important Questions on Mean of Grouped Data

HARD

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 1

Find the mean of the following frequency distribution by using step deviation method.

Class interval	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$5$	$3$	$4$	$7$	$2$	$6$	$13$

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 2

If assumed mean $(A) = 57.5$ , $\sum_{} f_{i} d_{i} = - 10$ and $\sum_{} f_{i} = 80$ , then Mean $=_____$

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 3

The height in cm of 50 boys are given below. Find the mean height.

Height	155	156	157	158	159	160
Frequency	4	15	8	6	12	5

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 4

Calculate the mean of the following distribution. Give your answer correct to one decimal place.

Class Interval	$5 - 15$	$15 - 25$	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$	$65 - 75$
Frequency	$6$	$11$	$7$	$4$	$4$	$2$	$1$

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 5

Using step-deviation method, calculate the mean marks of the following distribution:

Class interval	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$	$80 - 85$	$85 - 90$
Frequency	$5$	$20$	$10$	$10$	$9$	$6$	$12$	$8$

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 6

With usual meanings of notations, formula for assumed mean method for A.M. is

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 7

What will be value of standard deviation $(σ)$ of $2, 4, 6, 8, 10 [σ = \sqrt{\frac{\sum {(X - \bar{X})}^{2}}{N}}]$ .

HARD

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 8

Find the mean of the following data :

Class	$5 - 15$	$15 - 25$	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$	$65 - 75$
Frequency	$6$	$10$	$16$	$15$	$24$	$8$	$7$

HARD

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 9

Find the mean weight of packets of coffee using step deviation method:

Weight	$200 - 201$	$201 - 202$	$202 - 203$	$203 - 204$	$204 - 205$	$205 - 206$
Number of packets	$13$	$27$	$18$	$10$	$1$	$1$

HARD

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 10

Find the mean of the following data:

Class	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Frequency	$20$	$30$	$40$	$23$	$10$

HARD

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 11

Find the mean of the following frequency distribution using step-deviation method:

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$8$	$12$	$15$	$9$	$16$

HARD

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 12

Find the mean :

Marks	*$500 - 520$*	*$520 - 540$*	*$540 - 560$*	*$560 - 580$*	*$580 - 600$*
No. of students	*$12$*	*$14$*	*$8$*	*$6$*	*$10$*

EASY

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 13

What will be the mean deviation about median for the following data?

$18, 15, 20, 21, 23, 24$

EASY

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 14

If the quartile deviation is $16$ , then the quartile range is.

EASY

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 15

If the value of $1^{s t}$ quartile is $12$ and third quartile is $16$ then the coefficient of quartile deviation will be.

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 16

The following table shows the number of students and the time they utilised daily for their studies. Find the mean time (in $hours$ ), spent by students for their studies:

Time $(hours)$	No. of students
$0 - 2$	$8$
$2 - 4$	$14$
$4 - 6$	$18$
$6 - 8$	$10$
$8 - 10$	$10$

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 17

The following table shows the number of students and the time they utilised daily for their studies. Find the mean time (in $hours$ ), spent by students for their studies:

Time $(hours)$	No. of students
$0 - 2$	$8$
$2 - 4$	$14$
$4 - 6$	$18$
$6 - 8$	$10$
$8 - 10$	$10$

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 18

Find the mean of the following frequency distribution:-

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
$f_{i}$	$6$	$10$	$13$	$7$	$4$

HARD

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 19

The given is the marks obtained by $70$ boys in a class test.

Marks	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
No. of boys	$10$	$12$	$14$	$12$	$9$	$7$	$6$

Calculate the mean of marks rounded off to two decimal places.

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean of Grouped Data> Q 20

The following table gives the marks scored by students at a test examination in mathematics out of total marks $40$ .

$\begin{array}{lcccccccc} Marks & 0 - 5 & 5 - 10 & 10 - 15 & 15 - 20 & 20 - 25 & 25 - 30 & 30 - 35 & 35 - 40 \\ No. of students & 3 & 7 & 15 & 24 & 16 & 8 & 5 & 2 \end{array}$

Calculate the mean mark, correct to two decimal places.