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

Earn 100

Find the standard deviation, when variance of the data is $25$ .

50% studentsanswered this correctly

Important Questions on Measures of Dispersion

HARD

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

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

The S.D of

4, 5, 6, 7, \dots . ., 13

x

, then the S.D of

14, 15, \dots \dots 23

MEDIUM

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

The Standard Deviation of the numbers

31, 32, 33 \dots \dots . 46, 47

MEDIUM

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

Draw the necessary table to find the Standard Deviation for the data $20, 14, 16, 30, 21$ and $25$ .

MEDIUM

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

For a group of

100

students, the mean

{\bar{x}}_{1}

and the standard deviation

σ_{1}

of their marks were found to be

40

and

15

respectively. Later it was observed that the scores

40

and

50

were misread as

30

and

60

respectively. If the mean and the standard deviation with the corrected observations of the scores are

{\bar{x}}_{2}

and

σ_{2}

respectively, then

EASY

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

Standard deviation of a collection of data is $2 \sqrt{2}$ . If each value is multiplied by $3$ , then the standard deviation of the new data is:

MEDIUM

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

Let

X_{1}, X_{2}, \dots, X_{18}

be eighteen observations such that

\sum_{i = 1}^{18} (X_{i} - α) = 36

and

\sum_{i = 1}^{18} {(X_{i} - β)}^{2} = 90

, where

α

and

β

are distinct real numbers. If the standard deviation of these observations is

1

, then the value of

|α - β|

is _______.

MEDIUM

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

The mean and variance of

10

observations were calculated as

15

and

15

respectively by a student who took by mistake

25

instead of

15

for one observation. Then, the correct standard deviation is _______.

HARD

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

The standard deviations of

x_{i} (i = 1, 2, \dots . 10)

and

y_{i} (i = 1, \dots 10)

are respectively

a

and

b

\bar{x}, \bar{y}

are the means of these two sets of observations respectively. If

z_{i} = (x_{i} - \bar{x}) (y_{i} - \bar{y})

and

\sum_{i = 1}^{10} z_{i} = c

, then the standard deviation of the observations

(x_{i} - y_{i}), (i = 1, 2, \dots 10)

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 standard deviation of

1

9

natural numbers is ____________

MEDIUM

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

MEDIUM

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

Find

SD

1, 2, 3, 4, 5, 6, 7, 8, 9

EASY

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

Which of the following set of data has least standard deviation?

EASY

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

The mean and coefficient of variation of the marks of

n

students is

20

and

80

respectively. Find the value of variance of them.

HARD

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

In a given data set, mean of

40

observations is

50

and standard deviation is

12

. Two readings which were

20 & 25

mistakenly taken as

40

and

45

. Find correct variance of data set.

EASY

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

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 | =

MEDIUM

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

Σ_{i = 1}^{n} (x_{i} - a) = n

and

Σ_{i = 1}^{n} {(x_{i} - a)}^{2} = n a, (n, a > 1)

, then the standard deviation of

n

observations

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

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

Find the standard deviation, when variance of the data is 25.

Important Questions on Measures of Dispersion

Learn and Prepare for any exam you want !

Find the standard deviation, when variance of the data is $25$ .