Mathematics Crash Course JEE Main>Chapter 27 - Statistics>Level 2>Q 6

HARD

JEE Main

IMPORTANT

Earn 100

The first of the two samples in a group has $100$ items with mean $15$ and standard deviation $3 .$ If the whole group has $250$ items with mean $15.6$ and standard deviation $\sqrt{13.44},$ then the standard deviation of the second sample is:

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Important Questions on Statistics

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 27 - Statistics>Level 2>Q 7

For the set

A = \{x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\}

the variance is

4

and the mean is

2 .

For the set

B = \{y_{1}, y_{2}, y_{3}, y_{4}, y_{5}\}

the variance is

5

and the mean is

4 .

Then the variance of

A \cup B

is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 27 - Statistics>Level 2>Q 8

In any discrete series (when all the value are not same) the relationship between

M . D .

about mean and

S . D .

is-

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 27 - Statistics>Level 2>Q 9

The standard deviation in a variable

x

is

σ

. The standard deviation of the variable

\frac{a x + b}{c}

; where

a, b

and

c

are constants, is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 27 - Statistics>Level 2>Q 10

If each observation of a distribution, whose variance is

σ^{2}

, is multiplied by

λ

, then the

S . D .

of the new observations is:

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 27 - Statistics>Level 2>Q 11

If each observation of a distribution whose

S . D .

is

σ

, is increased by

λ

, then the variance of the new observations is:

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 27 - Statistics>Level 2>Q 12

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

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 27 - Statistics>Level 2>Q 13

A data consists of

n

observations:

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

If

\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

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 27 - Statistics>Level 2>Q 14

The first of the two samples have

100

items with mean

15

and

S . D . 3 .

If the whole group has

250

items with mean

15.6

and

S . D . = \sqrt{13.44}

then

S . D .

of the second group is