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 ^

EASY

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Rank correlation coefficient lies between

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Important Questions on Statistics

MEDIUM

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

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

EASY

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

For a given distribution the arithmetic mean is

15

and the standard deviation is

9

then the coefficient of variation is equal to

MEDIUM

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

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

MEDIUM

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

The variance of the first

50

even natural numbers is :

MEDIUM

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

Coefficient of variation of two distributions are

60

and

70

and their standard deviations are

21

and

16

respectively. Then their AM's are

HARD

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

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?

EASY

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

The coefficient of variation (C.V.) and the mean of a distribution are respectively

75

and

44

. Then the standard deviation of the distribution is

EASY

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

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

MEDIUM

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

Coefficient of variation of two distributions are

60

and

70

, and their standard deviation are

21

and

16

, respectively. What are their arithmetic means?

MEDIUM

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

If the numbers are

5, 1, 8, 7, 2

, then the coefficient of variation is

EASY

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

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

MEDIUM

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

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

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

If the standard deviation of the numbers

- 1, 0, 1, k

\sqrt{5}

where

k > 0,

then

k

is equal to

EASY

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

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

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

If the standard deviation of the random variable

X

\sqrt{3 p q}

and mean is

3 p

then

E (X^{2}) = \dots

HARD

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

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

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

Mean and standard deviation of

100

items are

50

and

4

respectively. The sum of squares of all the items is

EASY

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

The mean of a distribution is

14

and the standard deviation is

5

. What is the value of the coefficient of variation?

MEDIUM

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

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

Mathematics>Statistics and Probability>Statistics>Analysis of Frequency Distributions

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

Rank correlation coefficient lies between

Important Questions on Statistics

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