Let n ≥ 3 . A list of numbers 0 < x 1 < x 2 < … < x n has mean μ and standard deviation σ . A new list of numbers is made as follows: y 1 = 0 , y 2 = x 2 , … . , y n - 1 = x n - 1 , y n = x 1 + x n . The mean and the standard deviation of the new list are μ ^ & σ ^ . Which of the following is necessarily true?

μ may or may not be equal to μ ^

x 1 , x 2 , … , x n are n observations with mean x ¯ and standard deviation σ . Match the items of List-I with those of List-II List - I List - II (a) ∑ i = 1 n x i - x ¯ (i) Median (b) Variance σ 2 (ii) Coefficient of variation (c) Mean deviation (iiii) Zero (d) Measure used to find the homogeneity of given two series (iv) Mean of the absolute deviations from any measure of central tendency (v) Mean of the squares of the deviations from mean

a b c d ( iii ) ( v ) ( iv ) ( ii )

a b c d ( i ) ( ii ) ( iii ) ( iv )

a b c d ( i ) ( iv ) ( iii ) ( ii )

a b c d ( iii ) ( v ) ( ii ) ( i )

EASY

Earn 100

The standard deviation of the set ${10, 10, 10, 10, 10}$ is:

50% studentsanswered this correctly

Important Questions on Measures of Central Tendency

MEDIUM

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

The mean of five observations is

5

and their variance is

9.20 .

If three of the given five observations are

1, 3

and

8,

then a ratio of other two observations is

EASY

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

The standard deviation of the set $(10, 10, 10, 10, 10)$ is

MEDIUM

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

Mean and standard deviation of

100

items are

50

and

4

respectively. The sum of squares of all the items is

MEDIUM

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

Coefficient of variation of two distributions are

50

and

60

and their arithmetic means are

30

and

25

, respectively. Difference of their standard deviation is

EASY

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

The mean and the standard deviation

(S . D .)

of five observations are

9

and

0

, respectively. If one of the observation is increased such that the mean of the new set of five observations becomes

10

, then their

S . D .

MEDIUM

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

If the mean and the standard deviation of the data

3, 5, 7, a, b

are

5

and

2

respectively, then

a

and

b

are the roots of the equation:

EASY

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

The mean and variance of

n

observations

x_{1}, x_{2}, x_{3}, \dots, x_{n}

are

5

and

0

respectively. If

\sum_{i = 1}^{n} x_{i}^{2} = 400

, then the value of

n

is equal to

HARD

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

The variance of

50

observations is

7

. If each observation is multiplied by

6

and then

5

is subtracted from it, then the variance of the new data is

HARD

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

Let

n \geq 3

. A list of numbers

0 < x_{1} < x_{2} < \dots < x_{n}

has mean

μ

and standard deviation

σ

. A new list of numbers is made as follows:

y_{1} = 0, y_{2} = x_{2}, \dots ., y_{n - 1} = x_{n - 1}, y_{n} = x_{1} + x_{n}

. The mean and the standard deviation of the new list are

\hat{μ} & \hat{σ}

. Which of the following is necessarily true?

MEDIUM

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

The variance of the first

50

even natural numbers is :

MEDIUM

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

The means of two groups of observations

A

and

B

are

\vec{x}, \vec{y}

respectively and their standard deviations are respectively

2

and

3 .

In order that the group

A

is to be more consistent than the group

B,

\frac{\vec{y}}{\vec{x}} <

MEDIUM

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard 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

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

The standard deviation of the data

6, 7, 8, 9, 10

HARD

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

Let

X = \{x \in N : 1 \leq x \leq 17\}

and

Y = \{a x + b : x \in X and a, b \in R, a > 0\}

. If mean and variance of elements of

Y

are

17

and

216

respectively then

a + b

is equal to

MEDIUM

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

The variance of the data

2, 3, 5, 11, 13, 17, 19

is nearly

MEDIUM

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

The marks obtained by students $A$ and $B$ in $3$ examinations are given below

Marks of $A$	$30$	$20$	$40$
Marks of $B$	$70$	$0$	$5$

The ratio of the coefficient of variation of marks of $A$ and the coefficient of variation of marks of $B$ is

MEDIUM

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

$x_{1}, x_{2}, \dots, x_{n}$ are $n$ observations with mean $\bar{x}$ and standard deviation $σ$ . Match the items of List-I with those of List-II

	List - I		List - II
(a)	$\sum_{i = 1}^{n} (x_{i} - \bar{x})$	(i)	Median
(b)	Variance $(σ^{2})$	(ii)	Coefficient of variation
(c)	Mean deviation	(iiii)	Zero
(d)	Measure used to find the homogeneity of given two series	(iv)	Mean of the absolute deviations from any measure of central tendency
		(v)	Mean of the squares of the deviations from mean

MEDIUM

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

If the standard deviation of the numbers

- 1, 0, 1, k

\sqrt{5}

where

k > 0,

then

k

is equal to

MEDIUM

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

If the mean and standard deviation of

5

observations

x_{1}, x_{2}, x_{3}, x_{4}, x_{5}

are

10

and

3,

respectively, then the variance of

6

observations

x_{1}, x_{2}, \dots, x_{5}

and

- 50

is equal to

MEDIUM

Arithmetic>Data Interpretation>Measures of Central Tendency>Standard Deviation

If the standard deviation of the random variable

X

\sqrt{3 p q}

and mean is

3 p

then

E (X^{2}) = \dots

The standard deviation of the set {10, 10, 10, 10, 10} is:

Important Questions on Measures of Central Tendency

Learn and Prepare for any exam you want !

The standard deviation of the set ${10, 10, 10, 10, 10}$ is: