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 ^

MEDIUM

Earn 100

Find the standard deviation of the first $10$ natural numbers is

50% studentsanswered this correctly

Important Questions on Measures of Dispersion

HARD

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

The mean and the variance of five observations are

4

and

5.20

, respectively. If three of the observations are

3, 4

and

4

; then the absolute value of the difference of the other two observations, is :

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

An urn contains

5

red,

2

white and

3

black balls. Three balls are drawn, one-by-one, at random without replacement. Find the probability distribution of the number of white balls. Also, find the mean and the variance of the number of white balls drawn.

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

The variance of the first

50

even natural numbers is :

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

HARD

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

If the data

x_{1}, x_{2}, \dots x_{10}

is such that the mean of first four of these is

11,

the mean of the remaining six is

16

and the sum of squares of all of these is

2000

, then the standard deviation of this data is:

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

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

If the standard deviation of the numbers

- 1, 0, 1, k

\sqrt{5}

where

k > 0,

then

k

is equal to

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}

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

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

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?

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)

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

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

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

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

\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}

Find the standard deviation of the first 10 natural numbers is

Important Questions on Measures of Dispersion

Learn and Prepare for any exam you want !

Find the standard deviation of the first $10$ natural numbers is