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143 Questions
All Exams JEE Mains JEE Advanced
2021 JEE Mains MCQ
JEE Main 2021 (Online) 18th March Evening Shift
Let in a series of 2n observations, half of them are equal to a and remaining half are equal to $-$a. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively. Then the value of a2 + b2 is equal to :
A.
425
B.
250
C.
925
D.
650
2021 JEE Mains MCQ
JEE Main 2021 (Online) 16th March Morning Shift
Consider three observations a, b, and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?
A.
b2 = 3(a2 + c2) + 9d2
B.
b2 = 3(a2 + c2) $-$ 9d2
C.
b2 = 3(a2 + c2 + d2)
D.
b2 = a2 + c2 + 3d2
2020 JEE Mains MCQ
JEE Main 2020 (Online) 6th September Morning Slot
If $\sum\limits_{i = 1}^n {\left( {{x_i} - a} \right)} = n$ and $\sum\limits_{i = 1}^n {{{\left( {{x_i} - a} \right)}^2}} = na$
(n, a > 1) then the standard deviation of n
observations x1 , x2 , ..., xn is :
A.
$a$ – 1
B.
$n\sqrt {a - 1} $
C.
$\sqrt {n\left( {a - 1} \right)} $
D.
$\sqrt {a - 1} $
2020 JEE Mains MCQ
JEE Main 2020 (Online) 5th September Evening Slot
If the mean and the standard deviation of the
data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation :
A.
x2 – 20x + 18 = 0
B.
2x2 – 20x + 19 = 0
C.
x2 – 10x + 18 = 0
D.
x2 – 10x + 19 = 0
2020 JEE Mains MCQ
JEE Main 2020 (Online) 5th September Morning Slot
The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the remaining two observations is :
A.
2
B.
3
C.
1
D.
4
2020 JEE Mains MCQ
JEE Main 2020 (Online) 4th September Morning Slot
The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is :
A.
5
B.
3
C.
7
D.
9
2020 JEE Mains MCQ
JEE Main 2020 (Online) 3rd September Evening Slot
Let xi (1 $ \le $ i $ \le $ 10) be ten observations of a random variable X. If
$\sum\limits_{i = 1}^{10} {\left( {{x_i} - p} \right)} = 3$ and $\sum\limits_{i = 1}^{10} {{{\left( {{x_i} - p} \right)}^2}} = 9$
where 0 $ \ne $ p $ \in $ R, then the standard deviation of these observations is :
A.
${7 \over {10}}$
B.
${9 \over {10}}$
C.
${4 \over 5}$
D.
$\sqrt {{3 \over 5}} $
2020 JEE Mains MCQ
JEE Main 2020 (Online) 3rd September Morning Slot
For the frequency distribution :
Variate (x) :      x1   x2   x3 ....  x15
Frequency (f) : f1    f2   f3 ...... f15
where 0 < x1 < x2 < x3 < ... < x15 = 10 and
$\sum\limits_{i = 1}^{15} {{f_i}} $ > 0, the standard deviation cannot be :
A.
6
B.
1
C.
4
D.
2
2020 JEE Mains MCQ
JEE Main 2020 (Online) 2nd September Morning Slot
Let X = {x $ \in $ N : 1 $ \le $ x $ \le $ 17} and
Y = {ax + b: x $ \in $ X and a, b $ \in $ R, a > 0}. If mean
and variance of elements of Y are 17 and 216
respectively then a + b is equal to :
A.
7
B.
9
C.
-7
D.
-27
2020 JEE Mains MCQ
JEE Main 2020 (Online) 9th January Morning Slot
Let the observations xi (1 $ \le $ i $ \le $ 10) satisfy the
equations, $\sum\limits_{i = 1}^{10} {\left( {{x_1} - 5} \right)} $ = 10 and $\sum\limits_{i = 1}^{10} {{{\left( {{x_1} - 5} \right)}^2}} $ = 40.
If $\mu $ and $\lambda $ are the mean and the variance of the
observations, x1 – 3, x2 – 3, ...., x10 – 3, then
the ordered pair ($\mu $, $\lambda $) is equal to :
A.
(6, 6)
B.
(3, 3)
C.
(3, 6)
D.
(6, 3)
2020 JEE Mains MCQ
JEE Main 2020 (Online) 8th January Evening Slot
The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is
A.
3.98
B.
3.99
C.
4.01
D.
4.02
2020 JEE Mains MCQ
JEE Main 2020 (Online) 8th January Morning Slot
The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 resepectively. Each of these 10 observations is multiplied by p and then reduced by q, where p $ \ne $ 0 and q $ \ne $ 0. If the new mean and new s.d. become half of their original values, then q is equal to
A.
10
B.
-20
C.
-10
D.
-5
2019 JEE Mains MCQ
JEE Main 2019 (Online) 12th April Morning Slot
If the data x1, x2,......., x10 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 all of these is 2,000 ; then the standard deviation of this data is :
A.
$\sqrt 2 $
B.
2
C.
2$\sqrt 2 $
D.
4
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th April Evening Slot
If both the mean and the standard deviation of 50 observations x1, x2,..., x50 are equal to 16, then the mean of (x1 – 4)2 , (x2 – 4)2 ,....., (x50 – 4)2 is :
A.
400
B.
480
C.
380
D.
525
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th April Morning Slot
If for some x $ \in $ R, the frequency distribution of the marks obtained by 20 students in a test is :

Marks 2 3 5 7
Frequency (x + 1)2 2x - 5 x2 - 3x x

then the mean of the marks is
A.
3.0
B.
2.8
C.
2.5
D.
3.2
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th April Evening Slot
The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35 respectively, then ${y \over x}$ is equal to
A.
${7 \over 2}$
B.
${8 \over 3}$
C.
${9 \over 4}$
D.
${7 \over 3}$
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th April Morning Slot
If the standard deviation of the numbers –1, 0, 1, k is $\sqrt 5$ where k > 0, then k is equal to
A.
2$\sqrt 6 $
B.
$\sqrt 6 $
C.
$2\sqrt {{{5} \over 6}} $
D.
$2\sqrt {{{10} \over 3}} $
2019 JEE Mains MCQ
JEE Main 2019 (Online) 8th April Evening Slot
A student scores the following marks in five tests :

45, 54, 41, 57, 43.

His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is
A.
$100 \over {\sqrt 3}$
B.
$10 \over {\sqrt 3}$
C.
$10 \over3$
D.
$100 \over3$
2019 JEE Mains MCQ
JEE Main 2019 (Online) 8th April Morning Slot
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 :
A.
40
B.
48
C.
49
D.
45
2019 JEE Mains MCQ
JEE Main 2019 (Online) 12th January Evening Slot
The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :
A.
1
B.
7
C.
3
D.
5
2019 JEE Mains MCQ
JEE Main 2019 (Online) 12th January Morning Slot
If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :
A.
31
B.
50
C.
51
D.
30
2019 JEE Mains MCQ
JEE Main 2019 (Online) 11th January Morning Slot
The outcome of each of 30 items was observed; 10 items gave an outcome ${1 \over 2}$ – d each, 10 items gave outcome ${1 \over 2}$ each and the remaining 10 items gave outcome ${1 \over 2}$+ d each. If the variance of this outcome data is ${4 \over 3}$ then |d| equals :
A.
${2 \over 3}$
B.
${{\sqrt 5 } \over 2}$
C.
${\sqrt 2 }$
D.
2
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th January Evening Slot
If mean and standard deviation of 5 observations x1, x2, x3, x4, x5 are 10 and 3, respectively, then the variance of 6 observations x1, x2, ….., x5 and –50 is equal to
A.
582.5
B.
507.5
C.
586.5
D.
509.5
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th January Morning Slot
The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is -
A.
6 : 7
B.
10 : 3
C.
4 : 9
D.
5 : 8
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th January Evening Slot
A data consists of n observations : x1, x2, . . . . . . ., xn.    

If     $\sum\limits_{i = 1}^n {{{\left( {{x_i} + 1} \right)}^2}} = 9n$    and

$\sum\limits_{i = 1}^n {{{\left( {{x_i} - 1} \right)}^2}} = 5n,$

then the standard deviation of this data is :
A.
2
B.
$\sqrt 5 $
C.
5
D.
$\sqrt 7 $
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th January Morning Slot
5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, joined them. The variance (in cm2) of the height of these six students is :
A.
16
B.
22
C.
20
D.
18
2018 JEE Mains MCQ
JEE Main 2018 (Online) 16th April Morning Slot
The mean and the standard deviation(s.d.) of five observations are9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :
A.
0
B.
1
C.
2
D.
4
2018 JEE Mains MCQ
JEE Main 2018 (Offline)
If $\sum\limits_{i = 1}^9 {\left( {{x_i} - 5} \right)} = 9$ and

$\sum\limits_{i = 1}^9 {{{\left( {{x_i} - 5} \right)}^2}} = 45$, then the standard deviation of the 9 items
${x_1},{x_2},.......,{x_9}$ is
A.
3
B.
9
C.
4
D.
2
2018 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Evening Slot
If the mean of the data : 7, 8, 9, 7, 8, 7, $\lambda $, 8 is 8, then the variance of this data is :
A.
${7 \over 8}$
B.
1
C.
${9 \over 8}$
D.
2
2018 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Morning Slot
The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number $\lambda $ and then each of them is decreased by 25, their mean remains the same. Then $\lambda $ is equal to :
A.
${1 \over 3}$
B.
${2 \over 3}$
C.
${4 \over 3}$
D.
${10 \over 3}$
2017 JEE Mains MCQ
JEE Main 2017 (Online) 9th April Morning Slot
The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is :
A.
8.25
B.
8.50
C.
8.00
D.
9.00
2017 JEE Mains MCQ
JEE Main 2017 (Online) 8th April Morning Slot
The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is :
A.
25
B.
30
C.
35
D.
40
2016 JEE Mains MCQ
JEE Main 2016 (Online) 10th April Morning Slot
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 :
A.
2.4
B.
2.8
C.
2.5
D.
2.6
2016 JEE Mains MCQ
JEE Main 2016 (Online) 9th April Morning Slot
If the mean deviation of the numbers 1, 1 + d, ..., 1 +100d from their mean is 255, then a value of d is :
A.
10.1
B.
20.2
C.
10
D.
5.05
2016 JEE Mains MCQ
JEE Main 2016 (Offline)
If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?
A.
3$a$2 - 26$a$ + 55 = 0
B.
3$a$2 - 32$a$ + 84 = 0
C.
3$a$2 - 34$a$ + 91 = 0
D.
3$a$2 - 23$a$ + 44 = 0
2015 JEE Mains MCQ
JEE Main 2015 (Offline)
The mean of the data set comprising of 16 observations 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 :
A.
15.8
B.
14.0
C.
16.8
D.
16.0
2014 JEE Mains MCQ
JEE Main 2014 (Offline)
The variance of first 50 even natural numbers is
A.
833
B.
437
C.
${{437} \over 4}$
D.
${{833} \over 4}$
2013 JEE Mains MCQ
JEE Main 2013 (Offline)
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
A.
median
B.
mode
C.
variance
D.
mean
2012 JEE Mains MCQ
AIEEE 2012
Let x1, x2,........., xn be n observations, and let $\overline x $ be their arithematic mean and ${\sigma ^2}$ be their variance.

Statement 1 : Variance of 2x1, 2x2,......., 2xn is 4${\sigma ^2}$.
Statement 2 : : Arithmetic mean of 2x1, 2x2,......, 2xn is 4$\overline x $.
A.
Statement 1 is false, statement 2 is true
B.
Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
C.
Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
D.
Statement 1 is true, statement 2 is false
2011 JEE Mains MCQ
AIEEE 2011
If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals
A.
4
B.
5
C.
2
D.
3
2010 JEE Mains MCQ
AIEEE 2010
For two data sets, each of size 5, the variances 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
A.
${5 \over 2}$
B.
${11 \over 2}$
C.
6
D.
${13 \over 2}$
2009 JEE Mains MCQ
AIEEE 2009
If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is equal to
A.
20.0
B.
10.1
C.
20.2
D.
10.0
2009 JEE Mains MCQ
AIEEE 2009
Statement - 1 : The variance of first n even natural numbers is ${{{n^2} - 1} \over 4}$

Statement - 2 : The sum of first n natural numbers is ${{n\left( {n + 1} \right)} \over 2}$ and the sum of squares of first n natural numbers is ${{n\left( {n + 1} \right)\left( {2n + 1} \right)} \over 6}$
A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
B.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
C.
Statement-1 is true, Statement-2 is false
D.
Statement-1 is false, Statement-2 is true
2008 JEE Mains MCQ
AIEEE 2008
The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?
A.
a = 0, b = 7
B.
a = 5, b = 2
C.
a = 1, b = 6
D.
a = 3, b = 4
2007 JEE Mains MCQ
AIEEE 2007
The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is
A.
80
B.
60
C.
40
D.
20
2006 JEE Mains MCQ
AIEEE 2006
Suppose a population A has 100 observations 101, 102,........, 200, and another population B has 100 observations 151, 152,......., 250. If VA and VB represent the variances of the two populations, respectively, then ${{{V_A}} \over {{V_B}}}$ is
A.
1
B.
${9 \over 4}$
C.
${4 \over 9}$
D.
${2 \over 3}$
2005 JEE Mains MCQ
AIEEE 2005
If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately :
A.
20.5
B.
22.0
C.
24.0
D.
25.5
2005 JEE Mains MCQ
AIEEE 2005
Let x1, x2,...........,xn 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
A.
18
B.
15
C.
12
D.
9
2004 JEE Mains MCQ
AIEEE 2004
Consider the following statements:
(a) Mode can be computed from histogram
(b) Median is not independent of change of scale
(c) Variance is independent of change of origin and scale.
Which of these is/are correct?
A.
only (a)
B.
only (b)
C.
only (a) and (b)
D.
(a), (b) and (c)
2004 JEE Mains MCQ
AIEEE 2004
In a series of 2n observations, half of them equal $a$ and remaining half equal $–a$. If the standard deviation of the observations is 2, then $|a|$ equals
A.
2
B.
$\sqrt 2 $
C.
${1 \over n}$
D.
${{\sqrt 2 } \over n}$