EASY

JEE Main

IMPORTANT

Earn 100

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 :

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Important Questions on Statistics

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

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Statistics>JEE Main - 4 September 2020 Shift 1>Q 24

The mean and variance of

8

observations are

10

and

13.5,

respectively. If

6

of these observations are

5, 7, 10, 12, 14, 15,

then the absolute difference of the remaining two observations is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Statistics>JEE Main - 4 September 2020 Shift 2>Q 25

If the variance of the following frequency distribution is $50$ , then $x$ is equal to _____

Class	$10 - 20$	$20 - 30$	$30 - 40$
Frequency	$2$	$x$	$2$

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 22 - Statistics>JEE Main - 5 September 2020 Shift 1>Q 26

The mean and variance of

7

observations are

8

and

16

, respectively. If five observations are

2, 4, 10, 12, 14

then the absolute difference of the remaining two observations is :

Let in a series of 2n 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 a2+b2 is equal to :

Important Questions on Statistics

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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 :