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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In which year did Karl Pearson introduce the Pearson correlation coefficient?

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Important Questions on Statistics

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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

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}

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

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 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 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>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

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 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

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 :

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

In mammals, which blood vessel would normally carry the largest amount of urea?

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

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

Explain the term variation. What does a measure of variation serve? In the light of these, comment on some of the well-known measures of variation.

EASY

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

The following data gives the number of typing mistakes done by Radha during a week. Find the range of the data.

Day	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
Number of mistakes	$15$	$20$	$21$	$12$	$17$	$10$

HARD

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

Explain how measures of central tendency and measures of variations are complementary to each other in the context of analysis of data.

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

Explain and illustrate how the measure of variation afford a supplement to averages in the frequency distribution.

MEDIUM

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

For a series the value of mean deviation is

15

, the most likely value of its quartile derivation is

EASY

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

Find the range of the following data:

$19, 27, 15, 21, 33, 45, 7, 12, 20, 26$ .

In which year did Karl Pearson introduce the Pearson correlation coefficient?

Important Questions on Statistics

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