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JEE • MATHEMATICS • STATISTICS

Statistics practice · Easy

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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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Showing 1-30 of 312 questions
1 Easy
1 of 312
Application +4 | -1
If the mean of a set of observations x1,x2,…,xn{x_1},{x_2}, \ldots ,{x_n} is Xˉ,\bar X, then the mean of the observationsxi+2  i;i=1,  2,…,n{x_i} + 2\;i;i = 1,\;2, \ldots ,n is
View answer and explanation
Correct option: C
Xˉ+(n+1)\bar X + \left( {n + 1} \right)
Option C (Xˉ+(n+1)\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 312
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
3/53 / 5
Option D (3/53 / 5) is correct because the standard deviation is calculated using the given sums and the formula, resulting in 3/5.
3 Easy
3 of 312
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 312
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
48
Option C (48) is correct because it accurately calculates the product of the remaining two observations based on the given mean and variance.
5 Easy
5 of 312
Application +4 | -1
The geometric mean of 5,8,10,15,20,25,305,8,10,15,20,25,30 is
View answer and explanation
Correct option: B
10(9)1/710(9)^{1 / 7}
Option B (10(9)1/710(9)^{{1/7}}) is correct because it represents the geometric mean of the given numbers.
6 Easy
6 of 312
Application +4 | -1
If the S.D.\mathrm{S}.\mathrm{D}. of a variate XX is σ\sigma, then the S.D.\mathrm{S}.\mathrm{D}. of a  X+ba\;X + b is
View answer and explanation
Correct option: A
∣a∣    σ\left| a \right|\;\;\sigma
Option A (∣a∣  σ\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.
7 Easy
7 of 312
Application +4 | -1
The weighted mean of first nn natural numbers whose weights are equal is given by
View answer and explanation
Correct option: B
(n+1)/2(n+1) / 2
Option B ((n+1)2\frac{(n+1)}{2}) is correct because the weighted mean of the first n natural numbers with equal weights simplifies to the arithmetic mean.
8 Easy
8 of 312
Application +4 | -1
For a bivariate distribution (x,y)(x, y) if
∑x=50,∑y=60,∑xy=350,xˉ=5,yˉ=6.\sum x=50, \sum y=60, \sum x y=350, \bar{x}=5, \bar{y}=6 .

Variance of xx is 4 , variance of yy is 9 , then rxyr_{x y} equals
View answer and explanation
Correct option: C
56\frac{5}{6}
Option C (56\frac{5}{6}) is correct because it is the calculated correlation coefficient using the given data.
9 Easy
9 of 312
Application +4 | -1
If the variable takes the values 0,1,2,….n,  0,\mathrm{ }1,\mathrm{ }2,\mathrm{ } \ldots .n,\; with frequencies proportional to the binomial coefficients C(n,0),C(n,1),C(n,2),…..,C(n,n)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
n4\frac{n}{4}
Option D (n/4) is correct because the variance of the distribution is calculated to be n/4 using binomial coefficients.
10 Easy
10 of 312
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.
11 Easy
11 of 312
Application +4 | -1
For a series, the information available is n=10n=10, Σx=60\Sigma x=60 and Σx2=1000\Sigma x^2=1000. The standard deviation is
View answer and explanation
Correct option: A
8
Option A (8) is correct because the standard deviation is calculated using the formula and given values, resulting in 8.
12 Easy
12 of 312
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%60\%
Option A (60%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.
13 Easy
13 of 312
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
40
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.
14 Easy
14 of 312
Application +4 | -1
If x=X−Mx,y=Y−Myx=X-M_x, y=Y-M_y and Σxy=40,Σx2=80\Sigma x y=40, \Sigma x^2=80, Σy2=20\Sigma y^2=20. Then, coefficient of correlation between XX and YY is
View answer and explanation
Correct option: D
1
Option D (1) is correct because the correlation coefficient is calculated using the given sums of squares and cross-products, resulting in 1.
15 Easy
15 of 312
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.

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16 Easy
16 of 312
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
112\frac{{11}}{2}
The correct answer is B (112\frac{{11}}{2}) because it is the variance of the combined data set calculated using the given variances and means.
17 Easy
17 of 312
Application +4 | -1
The standard deviation of a variable x  is  10{x\;is\;10}. Then, the standard deviation of 50+5x50 + 5x is
View answer and explanation
Correct option: A
50
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.
18 Easy
18 of 312
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
14
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.
19 Easy
19 of 312
Analyzing +4 | -1
Statement 1: The variance of first nn odd natural numbers is n2−13\frac{n^2-1}{3}

Statement 2: The sum of first nn odd natural number is n2n^2 and the sum of square of first nn odd natural numbers is n(4n2+1)3\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.
20 Easy
20 of 312
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.
21 Easy
21 of 312
Application +4 | -1
The mean and standard deviation of 1,2,3,4,5,61,2,3,4,5,6 are
View answer and explanation
Correct option: A
72,3512\frac{7}{2}, \sqrt{\frac{35}{12}}
Option A (72,3512\frac{{7}}{{2}}, \sqrt{{\frac{{35}}{{12}}}}) is correct because the calculated mean is 7/2 and the standard deviation is 3512\sqrt{{\frac{{35}}{{12}}}} for the given data.
22 Easy
22 of 312
Application +4 | -1
If the data x1,x2,...,x10{x_1},{x_2},...,{x_{10}} is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of these is 2000, then the standard deviation of this data is
View answer and explanation
Correct option: B
2
Option B (2) is correct because it is the standard deviation calculated from the given data, using the formula for standard deviation.
23 Easy
23 of 312
Application +4 | -1
The mean of 5 observations is 5 and their variance is 124.
If three of the observations are 1, 2 and 6; then the mean
deviation from the mean of the data is :
View answer and explanation
Correct option: C
2.8
Option C (2.8) is correct. The mean deviation from the mean is calculated after finding the missing observations.
24 Easy
24 of 312
Application +4 | -1
In a moderately skewed distribution the values of mean and median are 5 and 6 respectively. The value of mode in such a situation is approximately equal to
View answer and explanation
Correct option: A
8
Option A (8) is correct because the mode can be estimated using the empirical relationship: Mode = 3 Median - 2 Mean.
25 Easy
25 of 312
Understanding +4 | -1
If byxb_{y x} and bxyb_{x y} are the regression coefficient of yy on xx and xx on yy respectively, then
View answer and explanation
Correct option: A
byx+bxy≥2r(x,y)b_{y x}+b_{x y} \geq 2 r(x, y)
Option A (byx+bxy≥2r(x,y)b_{yx} + b_{xy} \geq 2r(x, y)) is correct. The AM-GM inequality applied to regression coefficients shows that the sum of the regression coefficients is greater than or equal to twice the correlation coefficient.
26 Easy
26 of 312
Application +4 | -1
The variance of 6,8,10,12,146,8,10,12,14 is
View answer and explanation
Correct option: B
8
Option D (8) is correct because the variance is calculated as the average of the squared differences from the mean, which equals 8.
27 Easy
27 of 312
Application +4 | -1
If the mean of the data 7,7,9,7,8,7,λ,87,7,9,7,8,7, \lambda, 8 is 7, then the variance of this data is:
View answer and explanation
Correct option: D
114\frac{11}{4}
Option D (114\frac{{11}}{{4}}) is correct because it's the variance calculated using the given data and the calculated value of λ\lambda.
28 Easy
28 of 312
Application +4 | -1
1, 2, 4, 6, 8, 9 transformed into another series whose mean is 12. Two middle terms of the transformed series are
View answer and explanation
Correct option: D
11, 13
Option D (11, 13) is correct because adding 7 to each term shifts the mean to 12, and 11 and 13 are the middle terms of the transformed series.
29 Easy
29 of 312
Understanding +4 | -1
The SD of 15 items is 6 and if each item is decreases by 1 , then standard deviation will be
View answer and explanation
Correct option: D
6
Option D (6) is correct because standard deviation is a measure of dispersion and is not affected by adding or subtracting a constant from each data point.
30 Easy
30 of 312
Application +4 | -1
If       x1,x2,….,x18\;\;\;{x_1},{x_2}, \ldots .,{x_{18}} 18 are observation such that ∑j=118(xj−8)=9        and       ∑j=118(xj−8)2=45,\sum \limits_{j = 1}^{18} \left( {{x_j} - 8} \right) = 9\;\;\;\;and\,\;\;\;\sum \limits_{j = 1}^{18} {\left( {{x_j} - 8} \right)^2} = 45, then these standard derivation of these observations is
View answer and explanation
Correct option: D
32\frac{3}{2}
Option D (3/2) is correct because the standard deviation is calculated using the given sums and the formula for standard deviation.
Revision notes and key takeaways

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Key Takeaways

  • ✓ This set contains 312 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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