Back to STATISTICS

Your Progress

0 / 465 Answered

Correct

Incorrect

Accuracy

JEE • MATHEMATICS • STATISTICS

Statistics practice · Mixed difficulty

Try a question, then open “View answer” to check it. Sign in to submit answers and save progress.

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.

Take a chapter quiz →

Showing 1-30 of 465 questions

1 Easy

1 of 465

Application +4 | -1

If the mean of a set of observations

{x_1},{x_2}, \ldots ,{x_n}

\bar X,

then the mean of the observations

{x_i} + 2\;i;i = 1,\;2, \ldots ,n

View answer and explanation

Correct option: C

\bar X + \left( {n + 1} \right)

Option C (

\bar X + (n + 1)

) is correct because adding 2i to each observation increases the mean by the average of 2i, which is n+1.

2 Easy

2 of 465

Application +4 | -1

The sum of 10 items is 12 and sum of their squares is 18 , then standard deviation will be

View answer and explanation

Correct option: D

3 / 5

Option D (

3 / 5

) is correct because the standard deviation is calculated using the given sums and the formula, resulting in 3/5.

3 Easy

3 of 465

Application +4 | -1

In a family, there are 8 men, 7 women and 5 children whose mean ages separately are respectively 24,20 and 6 years. The mean age of the family is

View answer and explanation

Correct option: B

18.1 years

Option B (18.1 years) is correct because it is the weighted average age of the family, considering the number of men, women, and children.

4 Easy

4 of 465

Application +4 | -1

The mean and variance of 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

View answer and explanation

Correct option: C

Option C (48) is correct because it accurately calculates the product of the remaining two observations based on the given mean and variance.

5 Medium

5 of 465

Application +4 | -1

1,3,5, x, y

are 5 observations. Mean of these observations is 5 and variance is 8. Sum of the cubes of the two missing number equals:

View answer and explanation

Correct option: A

1072

Option A (1072) is correct because after calculating the missing numbers using the mean and variance, the sum of their cubes is 1072.

6 Medium

6 of 465

Application +4 | -1

If s.d. of a set of observations is 8 and if each observation is divided by

-2,

the s.d. of the new set of observations will be

View answer and explanation

Correct option: D

Option D (4) is correct because dividing each observation by -2 divides the standard deviation by the absolute value of -2, which is 2.

7 Easy

7 of 465

Application +4 | -1

The geometric mean of

5,8,10,15,20,25,30

View answer and explanation

Correct option: B

10(9)^{1 / 7}

Option B (

10(9)^{{1/7}}

) is correct because it represents the geometric mean of the given numbers.

8 Medium

8 of 465

Application +4 | -1

The mean of the distribution, in which the values of

X

are

1,2,.....n,

the frequency of each being unity is:

View answer and explanation

Correct option: C

\frac{{n + 1}}{2}

Option C (

\frac{{n + 1}}{2}

) is correct because the mean of the distribution is the sum of the values divided by the number of values.

9 Medium

9 of 465

Application +4 | -1

If a variable takes values

0,\;1,2,..,n

with frequencies

{q^n},{\;^n}{C_1}{q^{n - 1}}p,{\;^n}{C_2}{q^{n - 2}}{p^2}, \ldots {\;^n}{C_n}{p^n},

where

p + q = 1,

then the mean is

View answer and explanation

Correct option: A

np

Option A (

np

) is correct because the given distribution is a binomial distribution, and the mean of a binomial distribution is

np

10 Easy

10 of 465

Application +4 | -1

If the

\mathrm{S}.\mathrm{D}.

of a variate

X

\sigma

, then the

\mathrm{S}.\mathrm{D}.

a\;X + b

View answer and explanation

Correct option: A

\left| a \right|\;\;\sigma

Option A (

\left| a \right|\;\sigma

) is correct because the standard deviation of aX + b is the absolute value of a times the standard deviation of X.

11 Easy

11 of 465

Application +4 | -1

The weighted mean of first

n

natural numbers whose weights are equal is given by

View answer and explanation

Correct option: B

(n+1) / 2

Option B (

\frac{(n+1)}{2}

) is correct because the weighted mean of the first n natural numbers with equal weights simplifies to the arithmetic mean.

12 Medium

12 of 465

Application +4 | -1

Let sets

A

and

B

have 5 elements each. Let the mean of the elements in sets

A

and

B

5 and 8 respectively and the variance of the elements in sets

A

and

B

be 12 and 20 respectively. A new set

C

of 10 elements is formed by subtracting 3 from each element of

A

and adding 2 to each element of

B

. Then the sum of the mean and variance of the elements of

C

View answer and explanation

Correct option: C

Option C (38) is correct because it is the sum of the combined mean (6) and combined variance (32) of the new set C.

13 Easy

13 of 465

Application +4 | -1

For a bivariate distribution

(x, y)

\sum x=50, \sum y=60, \sum x y=350, \bar{x}=5, \bar{y}=6 .

Variance of

x

is 4 , variance of

y

is 9 , then

r_{x y}

equals

View answer and explanation

Correct option: C

\frac{5}{6}

Option C (

\frac{5}{6}

) is correct because it is the calculated correlation coefficient using the given data.

14 Easy

14 of 465

Application +4 | -1

If the variable takes the values

0,\mathrm{ }1,\mathrm{ }2,\mathrm{ } \ldots .n,\;

with frequencies proportional to the binomial coefficients

C\left( {n,0} \right),C\left( {n,1} \right),C\left( {n,2} \right), \ldots ..,C\left( {n,n} \right)

respectively, then the variance of the distribution is

View answer and explanation

Correct option: D

\frac{n}{4}

Option D (n/4) is correct because the variance of the distribution is calculated to be n/4 using binomial coefficients.

15 Easy

15 of 465

Understanding +4 | -1

The standard deviation is not affected by the change of

View answer and explanation

Correct option: A

Origin

Option A (Origin) is correct because the standard deviation is not affected by a change of origin.

Explore Other Chapters in MATHEMATICS

View All →

SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs

16 Easy

16 of 465

Application +4 | -1

For a series, the information available is

n=10

\Sigma x=60

and

\Sigma x^2=1000

. The standard deviation is

View answer and explanation

Correct option: A

Option A (8) is correct because the standard deviation is calculated using the formula and given values, resulting in 8.

17 Medium

17 of 465

Application +4 | -1

Coefficient of variation of two distributions are 50 and 60 and their arithmetic means are 30 and 25, respectively. Then, difference of their standard deviations is

View answer and explanation

Correct option: A

Option A (0) is correct because by using the formula for the coefficient of variation and the given values, we find that both standard deviations are equal, resulting in a difference of 0.

18 Easy

18 of 465

Application +4 | -1

Mean marks scored by the students of a class is 53. The mean marks of the girls is 55 and the mean marks of the boys is 50. What is the percentage of girls in the class?

View answer and explanation

Correct option: A

60\%

Option A (

60\%

) is correct because it is derived from setting up an equation based on the weighted average of the mean marks of boys and girls.

19 Easy

19 of 465

Understanding +4 | -1

If the median of 21 observations is 40 and if the observations greater than the median are increased by 6 then the median of the new data will be

View answer and explanation

Correct option: A

Option A (40) is correct because the median is the middle value, and increasing values above the median does not change the position of the middle value.

20 Hard

20 of 465

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.

21 Medium

21 of 465

Application +4 | -1

The mean of 10 numbers is 12.5 ; the mean of the first six is 15 and the last five is 10 . The sixth number is

View answer and explanation

Correct option: A

Option A (15) is correct because it calculates the sixth number by using the combined mean formula and solving for the unknown.

22 Easy

22 of 465

Application +4 | -1

x=X-M_x, y=Y-M_y

and

\Sigma x y=40, \Sigma x^2=80

\Sigma y^2=20

. Then, coefficient of correlation between

X

and

Y

View answer and explanation

Correct option: D

Option D (1) is correct because the correlation coefficient is calculated using the given sums of squares and cross-products, resulting in 1.

23 Easy

23 of 465

Application +4 | -1

Mean of 100 observations is 45 . It was later found that the two observations 19 and 31 were incorrectly recorded as 91 and 13 . The correct mean is

View answer and explanation

Correct option: B

44.46

Option B (44.46) is correct because it accurately adjusts the initial mean based on the corrected observations.

24 Easy

24 of 465

Application +4 | -1

For two data sets, each of size 5, the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

View answer and explanation

Correct option: B

\frac{{11}}{2}

The correct answer is B (

\frac{{11}}{2}

) because it is the variance of the combined data set calculated using the given variances and means.

25 Easy

25 of 465

Application +4 | -1

The standard deviation of a variable

{x\;is\;10}

. Then, the standard deviation of

50 + 5x

View answer and explanation

Correct option: A

Option D (50) is correct because multiplying a variable by a constant multiplies the standard deviation by the same constant, while adding a constant does not change the standard deviation.

26 Easy

26 of 465

Application +4 | -1

The mean of the data set comprising of 16 observation is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data is

View answer and explanation

Correct option: D

Option D (14) is correct because the new mean is calculated by subtracting the deleted value and adding the new values, then dividing by the new number of observations.

27 Easy

27 of 465

Analyzing +4 | -1

Statement 1: The variance of first

n

odd natural numbers is

\frac{n^2-1}{3}

Statement 2: The sum of first

n

odd natural number is

n^2

and the sum of square of first

n

odd natural numbers is

\frac{n\left(4 n^2+1\right)}{3}

View answer and explanation

Correct option: A

Statement 1 is true, Statement 2 is false.

Statement 1 is true and Statement 2 is false, therefore option A is the correct answer.

28 Easy

28 of 465

Understanding +4 | -1

The median of a set of 9 distinct observations is 20.5. if each of the largest 4 observations of the set is increased by 2, then the median of the new set

View answer and explanation

Correct option: D

Remains the same as that of the original set

Option D (Remains the same as that of the original set) is correct because the median is the middle value, and changing the largest 4 values doesn't affect the middle value in a set of 9 distinct observations.

29 Medium

29 of 465

Application +4 | -1

Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable

X

denote the number of rotten apples. If

\mu

and

\sigma^{2}

represent mean and variance of

X

, respectively, then

10\left(\mu^{2}+\sigma^{2}\right)

is equal to

View answer and explanation

Correct option: D

Option D (20) is correct because the calculated value of

10(\mu^2 + \sigma^2)

based on the mean and variance of the number of rotten apples drawn is 20.

30 Medium

30 of 465

Application +4 | -1

Let

{x_1},{x_2}, \ldots ..,{x_x}\;

be n observations such that

\sum x_i^2 = 400\;\;and\;\;\;\sum {x_i} = 80

. Then a possible value of n among the following is

View answer and explanation

Correct option: C

Option C (18) is correct because the condition for variance being non-negative leads to n >= 16, and 18 is the only option satisfying this.

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 465 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.

Showing 1-30 of 465 questions

Continue Your Practice

📚 Switch Set (ALL)

Chapter Sets

ALL 465 MCQs EASY 312 MCQs HARD 12 MCQs MEDIUM 141 MCQs

0 /465

0✓ 0✗

0% Accuracy