If x ¯ is the mean of n observations x 1 , x 2 , … , x n then the mean of the absolute deviations of these observations from x ¯ is

the mean proportion of the data

the standard deviation of the data

EASY

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"Mean has the least sampling variability" prove the mathematical property of mean

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Important Questions on Measures of Central Tendency

MEDIUM

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

Let

O

be the mean deviation of the first five odd natural numbers about their mean and

P

be the mean deviation of the first five prime numbers about their mean. Then

P - O =

HARD

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

The mean deviation about the mean for the following data is

Class Interval	$0 - 4$	$4 - 8$	$8 - 12$	$12 - 16$
Frequency	$4$	$3$	$2$	$1$

MEDIUM

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

The mean of three positive numbers is

9 .

The mean is larger than only one of these numbers. The mean deviation about mean is

2 .

The smallest number is

EASY

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

If the mean of the data

p, 6, 6, 7, 8, 11, 15, 16

, is

3

times

p

, then the mean deviation of the data from its mean is

EASY

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

What is the mean deviation about the mean for the following data?

$x_{i}$	$1$	$2$	$3$	$4$
$f_{i}$	$5$	$10$	$15$	$20$

MEDIUM

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

If the mean deviation about median for the number

3, 5, 7, 2 k, 12, 16, 21, 24

arranged in the ascending order, is

6

then the median is

MEDIUM

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

The approximate value of the mean deviation about the mean for the following data is

Class Interval	$0 - 2$	$2 - 4$	$4 - 6$	$6 - 8$	$8 - 10$
Frequency	$1$	$2$	$3$	$2$	$1$

EASY

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

Let

S

be the set of all values of

a_{1}

for which the mean deviation about the mean of

100

consecutive positive integers

a_{1}, a_{2}, a_{3}, \dots ., a_{100}

25

. Then

S

EASY

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

Sum of the squares of deviations is minimum when deviations are taken from

MEDIUM

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

If the mean deviation of the numbers

1, 1 + d, \dots, 1 + 100 d

from their mean is

255

, then a value of

d

is :

EASY

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

The mean deviation about the mean for the following data:

5, 6, 7, 8, 6, 9, 13, 12, 15

EASY

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

10

is the mean of the data

2, 3, 5, 18, 17, 15, 13, x, 9

and

7,

then the mean deviation of this data about its mean is

EASY

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

The mean deviation from the mean of the discrete data

1, 3, 4, 7, 11, 18, 29, 47, 78

MEDIUM

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

What will be the probable value of mean deviation when

Q_{3} = 40

and

Q_{1} = 15

EASY

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

\bar{x}

is the mean of

n

observations

x_{1}, x_{2}, \dots, x_{n}

then the mean of the absolute deviations of these observations from

\bar{x}

EASY

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

The probability distribution of random variable $X$ is given by:

$X$	$1$	$2$	$3$	$4$	$5$
$P (X)$	$K$	$2 K$	$2 K$	$3 K$	$K$

Let $p = P (1 < X < 4 ∣ X < 3)$ . If $5 p = λ K$ , then $λ$ is equal to

MEDIUM

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

The mean deviation of the data

2, 9, 9, 3, 6, 9, 4

from the mean is

MEDIUM

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

Let the data

4, 10, x, y, 27

be in the increasing order. If the median of the data is

18

and its mean deviation about mean is

7.6,

then the mean of this data is

EASY

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

M_{1}

and

M_{2}

are the mean deviations from mean and median of the first

15

even integers then

M_{1} + M_{2} =

EASY

Quantitative Aptitude>Data Interpretation>Measures of Central Tendency>Mean Deviation

The mean deviation from the mean of the set of observations,

- 1, 0, 4

"Mean has the least sampling variability" prove the mathematical property of mean

Important Questions on Measures of Central Tendency

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