1
MCQ (Single Correct Answer)

JEE Main 2018 (Online) 16th April Morning Slot

The mean and the standarddeviation(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

Explanation

Here mean = $$\overline x $$ = 9

$$ \Rightarrow $$   $$\overline x $$ = $${{\sum {{x_i}} } \over n}$$ = 9

$$ \Rightarrow $$  $${\sum {{x_i}} }$$ = 9 $$ \times $$ 5 = 45

Now, standard deviation = 0

$$\therefore\,\,\,$$ all the five terms are same i.e.; 9

Now for changed observation

$${\overline x _{new}}$$ = $${{36 + {x_5}} \over 5} = 10$$

$$ \Rightarrow $$   x5 = 14

$$\therefore\,\,\,$$ $$\sigma $$new = $$\sqrt {{{\sum {{{\left( {{x_i} - {{\overline x }_{new}}} \right)}^2}} } \over n}} $$

= $$\sqrt {{{4{{\left( {9 - 10} \right)}^2} + {{\left( {14 - 10} \right)}^2}} \over 5}} $$ = 2
2
MCQ (Single Correct Answer)

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

Explanation

Average height of 5 students,

$$\overline x = {{{x_1} + {x_2} + {x_3} + {x_4} + {x_5}} \over 5} = 150$$

$$ \Rightarrow \,\,\,\sum\limits_{i = 1}^5 {{x_i}} = 750$$

We know,

Variance $$\left( \sigma \right) = {{\sum {x_i^2} } \over 5} - {\left( {\overline x } \right)^2}$$

given that,

$${{\sum {x_i^2} } \over 5} - {\left( {150} \right)^2} = 18$$

$$ \Rightarrow \,\,\,\sum {x_i^2} = 112590$$

Height of new student, x6 $$=$$ 156 cm

New average height  $$\left( {{{\overline x }_{new}}} \right) = {{750 + 156} \over 6} = 151$$

New variance   $$ = {{\,\sum\limits_{i = 1}^6 {x_i^2} } \over 6} - {\left( {{{\overline x }_{new}}} \right)^2}$$

$$ = {{112590 + {{\left( {156} \right)}^2}} \over 6} - {\left( {151} \right)^2}$$

$$ = 22821 - 22801$$

$$ = 20$$
3
MCQ (Single Correct Answer)

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
$$\sqrt 7 $$

Explanation

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

$$\Rightarrow \sum\limits_{i = 1}^n {x_i^2} + 2\sum\limits_{i = 1}^n {{x_i}} + n = 9n\,\,\,\,\,...\,(1)$$

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

$$\Rightarrow \sum\limits_{i = 1}^n {x_i^2} - 2\sum\limits_{i = 1}^n {{x_i}} + n = 5n\,\,\,\,\,...\,(2)$$

Performing (1) + (2), we get

$$2\sum\limits_{i = 1}^n {x_i^2} + 2n = 14n$$

$$\sum\limits_{i = 1}^n {x_i^2} = 6n$$

Performing (1) $$-$$ (2), we get

$$ \Rightarrow 4\sum\limits_{i = 1}^n {{x_i}} = 4n$$

$$ \Rightarrow $$$$ \Rightarrow \sum\limits_{i = 1}^n {{x_i}} = n$$

S.D($$\sigma $$)$$ = \sqrt {{{\sum {x_i^2} } \over n} - {{\left( {\overline x } \right)}^2}} $$

$$\sigma $$ $$ = \sqrt {{{6n} \over n} - \left( 1 \right)} $$

$$\sigma $$ $$ = \sqrt 5 $$
4
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 10th January Morning Slot

In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is
A
42
B
102
C
1
D
38

Explanation

Let n(A) = number of students opted mathematic = 70,

n(B) = number of studens opted Physics = 46,

n(C) = number of students opted Chemistry = 28,

n(A $$ \cap $$ B) = 23,

n(B $$ \cap $$ C) = 9,

n(A $$ \cap $$ C) = 14,

n(A $$ \cap $$ B $$ \cap $$ C) = 4,

Now n(A $$ \cup $$ B $$ \cup $$ C)

= n(A) + n(B) + n(C) $$-$$ n(A $$ \cap $$ B) $$-$$ n(B $$ \cap $$ C)

      $$-$$ n(A $$ \cap $$ C) + n(A $$ \cap $$ B $$ \cap $$ C)

= 70 + 46 + 28 $$-$$ 23 $$-$$ 9 $$-$$ 14 + 4 = 102

So number of students not opted for any course

Total $$-$$ n(A $$ \cup $$ B $$ \cup $$ C)

= 140 $$-$$ 102 = 38

Questions Asked from Statistics

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Name Indicates No of Questions
AIEEE 2002 (1)
keyboard_arrow_right
AIEEE 2003 (2)
keyboard_arrow_right
AIEEE 2004 (2)
keyboard_arrow_right
AIEEE 2005 (2)
keyboard_arrow_right
AIEEE 2006 (1)
keyboard_arrow_right
AIEEE 2007 (1)
keyboard_arrow_right
AIEEE 2008 (1)
keyboard_arrow_right
AIEEE 2009 (2)
keyboard_arrow_right
AIEEE 2010 (1)
keyboard_arrow_right
AIEEE 2011 (1)
keyboard_arrow_right
AIEEE 2012 (1)
keyboard_arrow_right
JEE Main 2013 (Offline) (1)
keyboard_arrow_right
JEE Main 2014 (Offline) (1)
keyboard_arrow_right
JEE Main 2015 (Offline) (1)
keyboard_arrow_right
JEE Main 2016 (Offline) (1)
keyboard_arrow_right
JEE Main 2016 (Online) 9th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2016 (Online) 10th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2017 (Online) 8th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2017 (Online) 9th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2018 (Offline) (1)
keyboard_arrow_right
JEE Main 2018 (Online) 15th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2018 (Online) 15th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2018 (Online) 16th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th January Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 10th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 11th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 8th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 8th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th April Evening Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 10th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 8th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 8th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 9th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 2nd September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 3rd September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 3rd September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 4th September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 5th September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 5th September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 6th September Morning Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 16th March Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 18th March Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 20th July Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 20th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 25th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th July Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 26th August Morning Shift (1)
keyboard_arrow_right

EXAM MAP

Medical

NEET

Joint Entrance Examination

JEE Advanced JEE Main

Graduate Aptitude Test in Engineering

GATE CE GATE ECE GATE ME GATE IN GATE EE GATE CSE GATE PI