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JEE • MATHEMATICS • STATISTICS

Statistics practice · Medium

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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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Showing 1-30 of 141 questions

1 Medium

1 of 141

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.

2 Medium

2 of 141

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.

3 Medium

3 of 141

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.

4 Medium

4 of 141

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

5 Medium

5 of 141

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.

6 Medium

6 of 141

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.

7 Medium

7 of 141

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.

8 Medium

8 of 141

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.

9 Medium

9 of 141

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.

10 Medium

10 of 141

Application +4 | -1

A motor car when travelling from rest travels the first twentieth of a mile at

6 \mathrm{~m} / \mathrm{h}

the next three twentieths of the mile at

8,12,24 \mathrm{~m} / \mathrm{h}

respectively. But its average speed over the first one-fifth of a mile is not

12.5 \mathrm{~m} / \mathrm{h}

, then the correct average is

View answer and explanation

Correct option: A

9.6 \mathrm{~m} / \mathrm{h}

Option C (7.66, 28.02) is correct because it calculates the harmonic mean for the speeds and the geometric mean for the population increases.

11 Medium

11 of 141

Application +4 | -1

A man motors from

A

B

. In motoring a distance uphill he gets a mileage of only 10 miles per gallon of gasoline. On the return trip, he makes 15 miles per gallon, then the harmonic mean of his mileage (verify that this is the proper average to be used, here assuming that the distance from

A

B

is 60 miles) is

View answer and explanation

Correct option: A

Option A (12) is correct because the harmonic mean correctly averages the mileage rates for the round trip.

12 Medium

12 of 141

Application +4 | -1

The mean annual salaries paid to 1000 employees of a company was Rs. 3400 . The mean annual salaries paid to male and female employees were Rs. 200 and Rs. 4200, respectively. The percentage of males and females employed by the company are

View answer and explanation

Correct option: D

70,30

Option C (70,30) is correct because it represents the correct percentage of male and female employees calculated from the given mean salaries.

13 Medium

13 of 141

Application +4 | -1

Let

x_1, x_2, \ldots, x_{100}

be in an arithmetic progression, with

x_1=2

and their mean equal to 200 . If

y_i=i\left(x_i-i\right), 1 \leq i \leq 100

, then the mean of

y_1, y_2, \ldots

y_{100}

View answer and explanation

Correct option: C

10049.5

Option C (10049.5) is correct because it is the result of calculating the mean of the given series using the properties of arithmetic progressions and summation formulas.

14 Medium

14 of 141

Application +4 | -1

The AM of n numbers of a series is

{\bar X}

. If the sum of first

(n\; - 1)

terms is

k

then the

n{\;^{th}}

number is

View answer and explanation

Correct option: B

n\;\bar X - k

Option B (

n\;\bar X - k

) is correct because it represents the nth term calculated by subtracting the sum of the first (n-1) terms from the total sum of all n terms.

15 Medium

15 of 141

Understanding +4 | -1

In any discrete series (when all values are not same) the relationship between M.D. about mean and S.D. is

View answer and explanation

Correct option: D

\mathrm{M}.\mathrm{D}. \le \mathrm{S}.\mathrm{D}.

Option D (

\mathrm{M}.\mathrm{D}. \le \mathrm{S}.\mathrm{D}.

) is correct because the Mean Deviation (M.D.) is always less than or equal to the Standard Deviation (S.D.) in any discrete series.

Explore Other Chapters in MATHEMATICS

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

16 Medium

16 of 141

Application +4 | -1

\sum\limits_{{i=1}}^5 x_i^2=40 \& \sum\limits_{{i=6}}^{10} x_j^2=20

and mean of

x_1, x_2, \ldots \ldots x_5

, is 1 and mean of

x_6, x_7, \ldots \ldots . . . x_{10}

is 2 then variance of

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

View answer and explanation

Correct option: B

\frac{15}{4}

Option B (

\frac{15}{4}

) is correct because it is the variance calculated using the given sums of squares and means.

17 Medium

17 of 141

Application +4 | -1

The mean of 5 observation is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, then difference of the other two observations is

View answer and explanation

Correct option: A

Option A (5) is correct because by using the given mean and variance, we can set up equations to solve for the two unknown observations and then find their difference.

18 Medium

18 of 141

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},

the mean square deviation about

x = 0,

View answer and explanation

Correct option: B

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

Option D (n(n+1)/2) is incorrect. The correct answer is n(n+1)/4.

19 Medium

19 of 141

Application +4 | -1

n

observations on a variable

X_i

are

X_i=A+i B

for

i=1,2,3 \ldots . n

where

A, B

are real constants. The mean of these observation is

View answer and explanation

Correct option: A

A+B\left(\frac{n+1}{2}\right)

Option A (

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

) is correct because the mean of an arithmetic progression is the average of the first and last terms, which simplifies to the given expression.

20 Medium

20 of 141

Application +4 | -1

If the mean of 15 observations is 12 and standard deviation is 3. If 12 is replaced by 10 (in data) then the new mean is

\mu

and variance is

\sigma^2

then what is the value of

15\left(\mu+\mu^2+\sigma^2\right)

View answer and explanation

Correct option: A

2429

Option A (2429) is correct because it is the result of calculating

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

after replacing 12 with 10 in the data and finding the new mean and variance.

21 Medium

21 of 141

Application +4 | -1

The mean and standard deviation of 20 observations are found to be 10 and 2 , respectively. On respectively, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is

View answer and explanation

Correct option: C

\sqrt{3.96}

Option C (

\sqrt{{3.96}}

) is correct because it is the correct standard deviation calculated after adjusting for the error in the observation.

22 Medium

22 of 141

Understanding +4 | -1

Let

x_1, x_2, \ldots, x_n

\mathrm{n}

observations, and let

\bar{x}

be their arithmetic mean and

\sigma^2

be the variance.

Statement-1: Variance of

2 x_1, 2 x_2, \ldots, 2 x_n

4 \sigma^2

.

Statement-2: Arithmetic mean

2 x_1, 2 x_2, \ldots, 2 x_n

4 \bar{x}

View answer and explanation

Correct option: D

Statement-1 is true, statement-2 is false.

Option D is correct. Statement-1 is true because variance is multiplied by the square of the constant, and Statement-2 is false because the arithmetic mean is multiplied by 2, not 4.

23 Medium

23 of 141

Application +4 | -1

The means of five observations is 4 and their variance is 5.2. If three of these observations are 1,2 , and 6 , then the other two are:

View answer and explanation

Correct option: C

4 and 7

Option C (4 and 7) is correct because these values satisfy both the mean and variance conditions given in the problem.

24 Medium

24 of 141

Application +4 | -1

If the mean of the data :

7,8,9,7,8,7, \lambda, 8

is 8 , then the variance of this data is

View answer and explanation

Correct option: D

Option D (1) is correct. First, find the value of lambda using the mean. Then, calculate the variance using the formula.

25 Medium

25 of 141

Remembering +4 | -1

Angle between two lines of regression is given by

View answer and explanation

Correct option: B

{\tan ^{ - 1}}\left( {\frac{{{b_{yx}}.{b_{xy}} - 1}}{{{b_{yx}} + {b_{xy}}}}} \right)

Option B (

{\tan ^{ - 1}}\left( {\frac{{{b_{yx}}.{b_{xy}} - 1}}{{{b_{yx}} + {b_{xy}}}}} \right)

) is correct because it represents the correct formula for calculating the angle between two regression lines using their regression coefficients.

26 Medium

26 of 141

Application +4 | -1

The mean height of 25 male workers in a factory is
161 cms, and the mean height of 35 female workers
in the same factory is 158 cms. The combined mean
height of 60 workers in the factory is

View answer and explanation

Correct option: A

159.25

Option A (159.25) is correct because the combined mean is calculated by taking the weighted average of the means of the two groups.

27 Medium

27 of 141

Application +4 | -1

If the sum of the deviation 50 observation from 30 is 50, then the mean of these observations is

View answer and explanation

Correct option: D

Option D (31) is correct. The mean is calculated by using the sum of deviations from 30 to find the sum of the observations and then dividing by the number of observations.

28 Medium

28 of 141

Analyzing +4 | -1

Correlation coefficient

r

of two variables

x

and

y

is positive, when

View answer and explanation

Correct option: A

\sigma_{x+y} > \sigma_{x-y}

Option A (

\sigma_{x+y} > \sigma_{x-y}

) is correct because a positive correlation coefficient implies that the variance of the sum is greater than the variance of the difference.

29 Medium

29 of 141

Application +4 | -1

The standard deviation for the scores 1, 2, 3, 4, 5, 6 and 7 is 2. Then, the standard deviation of 12, 23, 34, 45, 56 , 67 and 78 is

View answer and explanation

Correct option: C

Option C (22) is correct because the standard deviation of a linearly transformed variable is the original standard deviation multiplied by the absolute value of the transformation factor.

30 Medium

30 of 141

Application +4 | -1

If the forces of 12,5 and 13 unit-wt balance at a point, two of them are inclined at

View answer and explanation

Correct option: C

90^{\circ}

Option C,

90^{\circ}

, is correct because the forces satisfy the Pythagorean theorem, indicating a right angle between the 5 and 12 unit forces.

Revision notes and key takeaways

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Key Takeaways

✓ This set contains 141 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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