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If the mean and standard deviation of $20$ observations $x_{1}, x_{2}, x_{3}, . . . . . . . ., x_{20}$ are $50$ and $10$ respectively, then ${\sum x_{i}^{2}}_{i = 1}^{i = 20}$ is equal to,

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Important Questions on Statistics

HARD

Mathematics>Mathematical Reasoning and Statistics>Statistics>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>Statistics>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>Statistics>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.

EASY

Mathematics>Mathematical Reasoning and Statistics>Statistics>Variance and Standard Deviation

The mean deviation from the mean of the set of observations,

- 1, 0, 4

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>Variance and Standard Deviation

The variance of the first

50

even natural numbers is :

EASY

Mathematics>Mathematical Reasoning and Statistics>Statistics>Variance and Standard Deviation

A random variable

X ∽ B (n, p) .

If values of mean and variance of

X

are

18

and

12

respectively then total number of possible values of

X

are

HARD

Mathematics>Mathematical Reasoning and Statistics>Statistics>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:

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>Variance and Standard Deviation

A data consists of

n

observations:

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

\sum_{i = 1}^{n} {(x_{i} + 1)}^{2} = 9 n

and

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

, then the standard deviation of this data is

EASY

Mathematics>Mathematical Reasoning and Statistics>Statistics>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>Statistics>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>Statistics>Variance and Standard Deviation

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

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Mathematics>Mathematical Reasoning and Statistics>Statistics>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>Statistics>Variance and 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

EASY

Mathematics>Mathematical Reasoning and Statistics>Statistics>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?

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Mathematics>Mathematical Reasoning and Statistics>Statistics>Variance and 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

Mathematics>Mathematical Reasoning and Statistics>Statistics>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 .

HARD

Mathematics>Mathematical Reasoning and Statistics>Statistics>Variance and Standard Deviation

A box contains

15

green and

10

yellow balls. If

10

balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is:

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>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>Statistics>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>Statistics>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}

If the mean and standard deviation of 20 observations x1,x2,x3,........,x20 are 50 and 10 respectively, then ∑xi2i=1i=20 is equal to,

Important Questions on Statistics

Learn and Prepare for any exam you want !

If the mean and standard deviation of $20$ observations $x_{1}, x_{2}, x_{3}, . . . . . . . ., x_{20}$ are $50$ and $10$ respectively, then ${\sum x_{i}^{2}}_{i = 1}^{i = 20}$ is equal to,