EASY

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The correct relationship between variance and the standard deviation is?

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Important Questions on Measures of Dispersion

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

The variance of

20

observations is

5 .

If each observation is multiplied by

3,

then what is the new variance of the resulting observations?

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

If the standard deviation of the numbers

- 1, 0, 1, k

\sqrt{5}

where

k > 0,

then

k

is equal to

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

The mean and variance of

20

observations are found to be

10

and

4,

respectively. On rechecking, it was found that an observation

9

was incorrect and the correct observation was

11,

then the correct variance is

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and 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

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and 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

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

The standard deviation of the data

6, 7, 8, 9, 10

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

The mean and variance for seven observations are

8

and

16

respectively. If

5

of the observations are

2, 4, 10, 12, 14,

then the product of the remaining two observations is

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

In a series of observations half of them equal to

a

and remaining half equal to

- a

. If the S.D. of the observations is

2

, then

| a | =

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

\sum_{i = 1}^{9} (x_{i} - 5) = 9

and

\sum_{i = 1}^{9} {(x_{i} - 5)}^{2} = 45

, then the standard deviation of the

9

items

x_{1}, x_{2}, \dots ., x_{9}

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

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

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

X

is a random variable such that

σ (X) = 2.6

then

σ (1 - 4 X)

is equal to

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of

10

to each of the students. Which of the following statistical measures will not change even after the grace marks were given ?

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

The standard deviation of a variable

x

10

. Then the standard deviation of

50 + 5 x

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and 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

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

Let

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

n

observations such that

Σ x_{i}^{2} = 400, Σ x_{i} = 80 .

Then, the possible value of

n

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

Consider three observations

a, b

and

c

such that

b = a + c

. If the standard deviation of

a + 2, b + 2, c + 2

d

, then which of the following is true?

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

Let in a series of

2 n

observations, half of them are equal to

a

and remaining half are equal to

- a

. Also by adding a constant

b

in each of these observations, the mean and standard deviation of new set become

5

and

20

, respectively. Then the value of

a^{2} + b^{2}

is equal to :

EASY

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

A student scores the following marks in five tests:

45,54,41,57,43

. His score is not known for the sixth test. If the mean score is

48

in the six tests, then the standard deviation of the marks in six tests is

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and Standard Deviation

The variance of the first

50

even natural numbers is :

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Measures of Dispersion>Variance and 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

The correct relationship between variance and the standard deviation is?

Important Questions on Measures of Dispersion

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