Mean

IMPORTANT

Mean: Overview

This topic covers concepts such as Measures of Central Tendency, Mean, Mean for Ungrouped Data, Mean for Grouped Data, Direct Method for Finding the Mean of Grouped Data, Assumed Mean Method for Finding the Mean of Grouped Data, etc.

Important Questions on Mean

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 1

Three values of a variable are $4, 5 and 7$ , if their frequencies are $(p - 2), (p + 1) and (p - 1)$ respectively and mean is $5.4$ , then value of $p$ is:

EASY

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 2

The average of $9$ observations is $15$ . If one more observation be added, the average becomes $16$ . Find the $10 th$ observation.

EASY

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 3

If the average of $10$ observations $x_{1}, x_{2}, \dots, x_{10}$ be $20$ then find the average of $x_{1} + 4, x_{2} + 8, x_{3} + 12 \dots, x_{10} + 40$

EASY

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 4

Find the mean of first $n$ even positive integers.

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IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 5

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
$0 - 2$	$8$
$2 - 4$	$14$
$4 - 6$	$18$
$6 - 8$	$10$
$8 - 10$	$10$

EASY

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 6

For a certain frequency distribution, the values of mean and median are $72$ and $78$ respectively. Find the value of mode.

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 7

Find the mean age of $100$ residents of a colony from the following data.

Age

(in years)

0 - 10

10 - 20

20 - 30

30 - 40

40 - 50

50 - 60

60 - 70

No. of
Persons

10

15

25

25

10

10

5

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IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 8

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> Q 9

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> Q 10

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.

EASY

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 11

When calculating the means of grouped and ungrouped data, there will be a variation.

EASY

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 12

Define Arithmetic mean and give their two demerits.

HARD

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 13

Find the arithmetic mean from the following frequency distribution:

Weight (in $kg$ )	$40 - 44$	$44 - 48$	$48 - 52$	$52 - 56$	$56 - 60$	$60 - 64$
No. of persons	$5$	$6$	$5$	$9$	$3$	$2$

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IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 14

Find the arithmetic mean of the following distribution:

$x$	$1$	$2$	$3$	$4$	$5$	$6$
$f$	$45$	$25$	$19$	$8$	$2$	$1$

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 15

Find the arithmetic mean of the following distribution:

$x$	$19$	$21$	$23$	$25$	$27$	$29$	$31$
$f$	$13$	$15$	$16$	$18$	$16$	$15$	$13$

MEDIUM

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 16

Find the arithmetic mean of the following distribution

$x$	$10$	$15$	$17$	$20$	$22$	$30$	$35$
$f$	$5$	$10$	$2$	$8$	$3$	$6$	$6$

EASY

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 17

Find the arithmetic mean of the following distribution

$x$	$5$	$6$	$7$	$8$	$9$
$f$	$4$	$8$	$14$	$11$	$3$

EASY

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 18

Give difference between arithmetic mean and weighted arithmetic mean

EASY

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 19

Positional mean is:

HARD

IMPORTANT

Mathematics>Measures of Central Tendency>Mean> Q 20

Find the mean of the following frequency distribution.

Class interval	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Frequency	$10$	$25$	$28$	$12$	$10$	$15$

Mean

Mean: Overview

Important Questions on Mean

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