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JEE • MATHEMATICS • STATISTICS

Statistics practice · Hard

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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1 Hard

1 of 12

Analyzing +4 | -1

The mean square deviation of a set of

\mathrm{m}

observations

y_1, y_2 \ldots . y_m

about a point

K

is defined as

\frac{1}{m} \sum\limits_{{i=1}}^{m}\left(y_i-k\right)^2

. The mean square deviation about -3 and 3 are 16 and 8 respectively, then standard deviation of this set of observation?

View answer and explanation

Correct option: A

\frac{\sqrt{23}}{3}

Option A (

\frac{\sqrt{23}}{3}

) is correct because it is the standard deviation calculated from the given mean square deviations about -3 and 3.

2 Hard

2 of 12

Application +4 | -1

If the values of regression coefficients are -0.33 and -1.33, then the value of coefficients of correlation between the two variables, is

View answer and explanation

Correct option: B

-0.66

Option B (-0.66) is correct because the correlation coefficient is the negative square root of the product of the regression coefficients.

3 Hard

3 of 12

Application +4 | -1

In a set of

2 \mathrm{n}

observations, half of them are equal to '

\mathrm{a}

' and the remaining half are equal to '-

\mathrm{a}^{\prime}

. If the standard deviation of all the observations is 2 ; then the value of

|a|

is :

View answer and explanation

Correct option: A

Option A (2) is correct. The standard deviation is calculated using the given information about the observations.

4 Hard

4 of 12

Application +4 | -1

The regression coefficient of

y

on x is 2/3 and that of

x

y

is 4/3 .The acute angle between the two regression lines is

{\tan ^{ - 1}}k,\;

where

k

is equal to

View answer and explanation

Correct option: C

1/18

Option C (1/18) is correct because the acute angle between the regression lines is calculated using the given regression coefficients.

5 Hard

5 of 12

Application +4 | -1

Z = aX + bY

and

r

be the correlation coefficient between

X\;and\;Y

, then

\sigma _Z^2

is equal to

View answer and explanation

Correct option: A

{a^2}\sigma _X^2 + {b^2}\sigma _Y^2 + 2abr{\sigma _X}{\sigma _Y}

The correct answer is A (

{a^2}\sigma _X^2 + {b^2}\sigma _Y^2 + 2abr{\sigma _X}{\sigma _Y}

) because it represents the variance of a linear combination of two random variables, considering their correlation.

6 Hard

6 of 12

Application +4 | -1

\sum\limits_{{i=1}}^5\left(x_i-10\right)=5

and

\sum\limits_{{i=1}}^5\left(x_i-10\right)^2=25

then standard deviation of observations

2 x_1+7

2 x_2+7,2 x_3+7,2 x_4+7

and

2 x_5+7

is equal to:

View answer and explanation

Correct option: C

Option C (4) is correct because the standard deviation of

2x_i + 7

is twice the standard deviation of

x_i

, and the standard deviation is not affected by the change of origin.

7 Hard

7 of 12

Application +4 | -1

If the mean deviation about the median of the numbers

a

2 a, \ldots \ldots, 50 a

is 50 , then

|a|

equals

View answer and explanation

Correct option: B

Option B (4) is correct. The mean deviation about the median is calculated using the given information.

8 Hard

8 of 12

Application +4 | -1

If a variable X takes values

0,1,2, \ldots ,n

with frequencies proportional to the binomial coefficients

^n{C_0},{\;^n}{C_1},{\;^n}{C_2}, \ldots ,{\;^n}{C_n},

then the

\mathrm{Var\;}\left( X \right)

View answer and explanation

Correct option: C

\frac{n}{4}

Option C (

\frac{n}{4}

) is correct because the variance of a binomial distribution with frequencies proportional to binomial coefficients is

\frac{n}{4}

9 Hard

9 of 12

Application +4 | -1

If the angle

\alpha

between two forces of equal magnitude is reduced to

\alpha-\frac{\pi}{3}

, then the magnitude of their resultant becomes

\sqrt{3}

times of the earlier one. The angle

\alpha

View answer and explanation

Correct option: B

2 \pi / 3

Option B,

\frac{2 \pi}{3}

, is correct because it satisfies the condition that the resultant becomes

\sqrt{3}

times the earlier one when the angle is reduced by

\frac{\pi}{3}

10 Hard

10 of 12

Application +4 | -1

If the mean of

4,7,2,8,6

and

a

is 7 , then the mean deviation from the median of these observations is

View answer and explanation

Correct option: D

Option D (3) is correct. The mean deviation from the median is calculated after finding the missing observation and the median.

11 Hard

11 of 12

Analyzing +4 | -1

If the standard deviation of 10 observations

x_1, x_2, \ldots . ., x_{10}

is 4 and that of another set of 10 observations

y_1, y_2, \ldots \ldots y_{10}

is 3 and also

X_i=\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right) . \bar{x}

is mean of all

x_i

's and

\bar{y}

is mean all

y_i

's and

\sum\limits_{{i=1}}^{10} X_i=80

. Then standard deviation of observations

x_1-y_1, x_2-y_2, \ldots \ldots, x_{10}-y_{10}

View answer and explanation

Correct option: B

Option B (3) is correct because the standard deviation of the difference of two sets of observations can be found using the given standard deviations and the sum of the product of deviations from the means.

12 Hard

12 of 12

Application +4 | -1

The centre of mass of a rod of length '

a

\mathrm{cm}

whose density varies as the square of the distance from one end, will be at a distance

View answer and explanation

Correct option: D

\frac{3 a}{4}

from this end

Option D,

\frac{3a}{4}

from this end, is correct because it is the calculated center of mass for a rod with density varying as the square of the distance from one end.

Revision notes and key takeaways

Review STATISTICS in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 12 single-correct-answer MCQs on STATISTICS.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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