HARD

JEE Main

IMPORTANT

Earn 100

Consider the statistics of two sets of observations as follows:

Size Mean Variance

Observation I $10$ $2$ $2$

Observation II $n$ $3$ $1$

If the variance of the combined set of these two observations is $\frac{17}{9},$ then the value of $n$ is equal to ________.

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Important Questions on Statistics

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Statistics>JEE Main 17 March 2021 Shift 2>Q 16

Consider a set of

3 n

numbers having variance

4 .

In this set, the mean of first

2 n

numbers is

6

and the mean of the remaining

n

numbers is

3 .

A new set is constructed by adding

1

into each of the first

2 n

numbers, and subtracting

1

from each of the remaining

n

numbers. If the variance of the new set is

k,

then

9 k

is equal to ______.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Statistics>JEE Main 18 March 2021 Shift 1>Q 17

The mean age of

25

teachers in a school is

40

years. A teacher retires at the age of

60

years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is

39

years, then the age (in years) of the newly appointed teacher is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Statistics>JEE Main 18 March 2021 Shift 2>Q 18

Let in a series of

2 n

observations, half of them are equal to

a

and remaining half are equal to

- a

. Also by adding a constant

b

in each of these observations, the mean and standard deviation of new set become

5

and

20

, respectively. Then the value of

a^{2} + b^{2}

is equal to :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Statistics>JEE Main - 24 Feb 2021 Shift 2>Q 19

If the variance of

10

natural numbers

1, 1, 1, \dots, 1, k

is less than

10,

then the maximum possible integral value of

k

is ___________.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Statistics>JEE Main - 26 Feb 2021 Shift 2>Q 20

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 _______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Statistics>JEE Main - 2 September 2020 Shift 1>Q 21

Let

X = \{x \in N : 1 \leq x \leq 17\}

and

Y = \{a x + b : x \in X and a, b \in R, a > 0\}

. If mean and variance of elements of

Y

are

17

and

216

respectively then

a + b

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Statistics>JEE Main - 2 September 2020 Shift 2>Q 22

If the variance of the terms in an increasing

A . P .

b_{1} b_{2}, b_{3}, \dots \dots . ., b_{11}

90

, then the common difference of this

A . P .

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Statistics>JEE Main - 3 September 2020 Shift 1>Q 23

For the frequency distribution: Variate

(x) : x_{1}, x_{2}, x_{3}, \dots, x_{15}

Frequency

(f) : f_{1}, f_{2}, f_{3}, \dots, f_{15}

where

0 < x_{1} < x_{2} < x_{3} < \dots < x_{15} = 10

and

\sum_{i = 1}^{15} f_{i} > 0,

the standard deviation cannot be

	Size	Mean	Variance
Observation I	$10$	$2$	$2$
Observation II	$n$	$3$	$1$

Consider the statistics of two sets of observations as follows: Size Mean Variance Observation I 10 2 2 Observation II n 3 1 If the variance of the combined set of these two observations is 179, then the value of n is equal to ________.

Important Questions on Statistics

Learn and Prepare for any exam you want !

Consider the statistics of two sets of observations as follows:

Size Mean Variance

Observation I $10$ $2$ $2$

Observation II $n$ $3$ $1$

If the variance of the combined set of these two observations is $\frac{17}{9},$ then the value of $n$ is equal to ________.