Let N denote the set of all natural numbers. Define two binary relations on N as R 1 = x , y ∈ N × N : 2 x + y = 10 and R 2 = x , y ∈ N × N : x + 2 y = 10 . Then

both R 1 and R 2 are transitive relations

both R 1 and R 2 are symmetric relations

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What symbol is commonly used to represent the correlation coefficient?

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Important Questions on Statistics

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.

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

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:

HARD

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

{\sum_{i = 1}^{20} (\frac{^{20} C_{i - 1}}{^{20} C_{i} +^{20} C_{i - 1}})}^{3} = \frac{k}{21},

then

k

equals

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

Let

N

denote the set of all natural numbers. Define two binary relations on

N

R_{1} = \{(x, y) \in N \times N : 2 x + y = 10\}

and

R_{2} = \{(x, y) \in N \times N : x + 2 y = 10\}

. Then

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

Suppose that

20

pillars of the same height have been erected along the boundary of circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is:

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

\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>Statistics>Variance and Standard Deviation

There are

m

men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by

84

, then the value of

m

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

HARD

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

If in a regular polygon the number of diagonals is

54

, then the number of sides of this polygon is:

MEDIUM

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

The sum of the series

1 + 2 \times 3 + 3 \times 5 + 4 \times 7 + \dots

upto

11^{t h}

term is:

MEDIUM

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

A committee of

11

member is to be formed from

8

males and

5

females. If

m

is the number of ways the committee is formed with at least

6

males and

n

is the number of ways the committee is formed with at least

3

females, then

MEDIUM

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

The value of

\sum_{r = 1}^{10} r \cdot \frac{{}^{n}C_{r}}{{}^{n}C_{r - 1}}

is equal to

EASY

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

The Number of ways of choosing

10

objects out of

31

objects of which

10

are identical and the remaining

21

are distinct, 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 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>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 ?

What symbol is commonly used to represent the correlation coefficient?

Important Questions on Statistics

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