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JEE Mains Previous Year Questions 
(2021-2024): Statistics 
2024 
Q1 - 2024 (01 Feb Shift 1) 
Let the median and the mean deviation about the median of 7 observation 
170,125,230,190,210, a, b be 170 and 
205
7
 respectively. Then the mean deviation about 
the mean of these 7 observations is : 
(1) 31 
(2) 28 
(3) 30 
(4) 32 
Q2 - 2024 (01 Feb Shift 2) 
Consider 10 observationx
1
, ?? 2,…
, ?? 10
. such that ?
?? =1
10
?( ?? ?? - ?? )= 2 and ?
?? =1
10
?( ?? ?? - ?? )
2
= 40, 
where ?? , ?? are positive integers. Let the mean and the variance of the observations be 
6
5
 
and 
84
25
 respectively. The 
?? ?? is equal to : 
(1) 2 
(2) 
3
2
 
(3) 
5
2
 
(4) 1 
Q3 - 2024 (27 Jan Shift 1) 
Let ?? 1
, ?? 2
, … ?? 10
 be 10 observations such that ?
k=1
10
?a
k
= 50 and ?
?k<j
?a
k
· a
j
= 1100. Then 
the standard deviation of ?? 1
, ?? 2
, … , ?? 10
 is equal to : 
(1) 5 
(2) v 5 
(3) 10 
Page 2


JEE Mains Previous Year Questions 
(2021-2024): Statistics 
2024 
Q1 - 2024 (01 Feb Shift 1) 
Let the median and the mean deviation about the median of 7 observation 
170,125,230,190,210, a, b be 170 and 
205
7
 respectively. Then the mean deviation about 
the mean of these 7 observations is : 
(1) 31 
(2) 28 
(3) 30 
(4) 32 
Q2 - 2024 (01 Feb Shift 2) 
Consider 10 observationx
1
, ?? 2,…
, ?? 10
. such that ?
?? =1
10
?( ?? ?? - ?? )= 2 and ?
?? =1
10
?( ?? ?? - ?? )
2
= 40, 
where ?? , ?? are positive integers. Let the mean and the variance of the observations be 
6
5
 
and 
84
25
 respectively. The 
?? ?? is equal to : 
(1) 2 
(2) 
3
2
 
(3) 
5
2
 
(4) 1 
Q3 - 2024 (27 Jan Shift 1) 
Let ?? 1
, ?? 2
, … ?? 10
 be 10 observations such that ?
k=1
10
?a
k
= 50 and ?
?k<j
?a
k
· a
j
= 1100. Then 
the standard deviation of ?? 1
, ?? 2
, … , ?? 10
 is equal to : 
(1) 5 
(2) v 5 
(3) 10 
(4) v 115 
Q4 - 2024 (27 Jan Shift 2) 
The mean and standard deviation of 15 observations were found to be 12 and 3 
respectively. On rechecking it was found that an observation was read as 10 in place of 
12 . If ?? and ?? 2
 denote the mean and variance of the correct observations respectively, 
then 15( ?? + ?? 2
+ ?? 2
) is equal to 
Q5 - 2024 (29 Jan Shift 1) 
If the mean and variance of the data 65,68,58,44,48,45,60, ?? , ?? , 60 where ?? > ?? are 56 
and 66.2 respectively, then ?? 2
+ ?? 2
 is equal to 
Q6 - 2024 (29 Jan Shift 2) 
If the mean and variance of five observations are 
24
5
 and 
194
25
 respectively and the mean of 
first four observations is 
7
2
, then the variance of the first four observations in equal to 
(1) 
4
5
 
(2) 
77
12
 
(3) 
5
4
 
(4) 
105
4
 
Q7 - 2024 (30 Jan Shift 1) 
Let ?? denote the median of the following frequency distribution. 
Class 0 - 4 4 - 8 8 - 12 12 - 16 16 - 20 
Frequency 3 9 10 8 6 
 
Then 20M is equal to : 
(1) 416 
(2) 104 
(3) 52 
(4) 208 
Page 3


JEE Mains Previous Year Questions 
(2021-2024): Statistics 
2024 
Q1 - 2024 (01 Feb Shift 1) 
Let the median and the mean deviation about the median of 7 observation 
170,125,230,190,210, a, b be 170 and 
205
7
 respectively. Then the mean deviation about 
the mean of these 7 observations is : 
(1) 31 
(2) 28 
(3) 30 
(4) 32 
Q2 - 2024 (01 Feb Shift 2) 
Consider 10 observationx
1
, ?? 2,…
, ?? 10
. such that ?
?? =1
10
?( ?? ?? - ?? )= 2 and ?
?? =1
10
?( ?? ?? - ?? )
2
= 40, 
where ?? , ?? are positive integers. Let the mean and the variance of the observations be 
6
5
 
and 
84
25
 respectively. The 
?? ?? is equal to : 
(1) 2 
(2) 
3
2
 
(3) 
5
2
 
(4) 1 
Q3 - 2024 (27 Jan Shift 1) 
Let ?? 1
, ?? 2
, … ?? 10
 be 10 observations such that ?
k=1
10
?a
k
= 50 and ?
?k<j
?a
k
· a
j
= 1100. Then 
the standard deviation of ?? 1
, ?? 2
, … , ?? 10
 is equal to : 
(1) 5 
(2) v 5 
(3) 10 
(4) v 115 
Q4 - 2024 (27 Jan Shift 2) 
The mean and standard deviation of 15 observations were found to be 12 and 3 
respectively. On rechecking it was found that an observation was read as 10 in place of 
12 . If ?? and ?? 2
 denote the mean and variance of the correct observations respectively, 
then 15( ?? + ?? 2
+ ?? 2
) is equal to 
Q5 - 2024 (29 Jan Shift 1) 
If the mean and variance of the data 65,68,58,44,48,45,60, ?? , ?? , 60 where ?? > ?? are 56 
and 66.2 respectively, then ?? 2
+ ?? 2
 is equal to 
Q6 - 2024 (29 Jan Shift 2) 
If the mean and variance of five observations are 
24
5
 and 
194
25
 respectively and the mean of 
first four observations is 
7
2
, then the variance of the first four observations in equal to 
(1) 
4
5
 
(2) 
77
12
 
(3) 
5
4
 
(4) 
105
4
 
Q7 - 2024 (30 Jan Shift 1) 
Let ?? denote the median of the following frequency distribution. 
Class 0 - 4 4 - 8 8 - 12 12 - 16 16 - 20 
Frequency 3 9 10 8 6 
 
Then 20M is equal to : 
(1) 416 
(2) 104 
(3) 52 
(4) 208 
The variance ?? 2
 of the data 
?? ?? 0 1 5 6 10 12 17 
?? ?? 3 2 3 2 6 3 3 
 
Is 
Q9 - 2024 (31 Jan Shift 2) 
Let the mean and the variance of 6 observation a, b, 68,44,48,60 be 55 and 194 , 
respectively if ?? > ?? , then ?? + 3?? is 
(1) 200 
(2) 190 
(3) 180 
(4) 210 
Answer Key 
Q1 (3)  ???? (1) Q3 (2) Q4 (2521) 
Q5 (6344) Q6 (3) Q7 (4) Q8 (29) 
Q9 (3)    
 
Solutions 
Q1 
 Median = 170 ? 125 , a, b, 170,190,210,230 
Mean deviation about 
Median = 
0 + 45 + 60 + 20 + 40 + 170 - ?? + 170 - ?? 7
=
205
7
 
? a + b = 300 
Mean =
170+125+230+190+210+?? +?? 7
= 175 
Page 4


JEE Mains Previous Year Questions 
(2021-2024): Statistics 
2024 
Q1 - 2024 (01 Feb Shift 1) 
Let the median and the mean deviation about the median of 7 observation 
170,125,230,190,210, a, b be 170 and 
205
7
 respectively. Then the mean deviation about 
the mean of these 7 observations is : 
(1) 31 
(2) 28 
(3) 30 
(4) 32 
Q2 - 2024 (01 Feb Shift 2) 
Consider 10 observationx
1
, ?? 2,…
, ?? 10
. such that ?
?? =1
10
?( ?? ?? - ?? )= 2 and ?
?? =1
10
?( ?? ?? - ?? )
2
= 40, 
where ?? , ?? are positive integers. Let the mean and the variance of the observations be 
6
5
 
and 
84
25
 respectively. The 
?? ?? is equal to : 
(1) 2 
(2) 
3
2
 
(3) 
5
2
 
(4) 1 
Q3 - 2024 (27 Jan Shift 1) 
Let ?? 1
, ?? 2
, … ?? 10
 be 10 observations such that ?
k=1
10
?a
k
= 50 and ?
?k<j
?a
k
· a
j
= 1100. Then 
the standard deviation of ?? 1
, ?? 2
, … , ?? 10
 is equal to : 
(1) 5 
(2) v 5 
(3) 10 
(4) v 115 
Q4 - 2024 (27 Jan Shift 2) 
The mean and standard deviation of 15 observations were found to be 12 and 3 
respectively. On rechecking it was found that an observation was read as 10 in place of 
12 . If ?? and ?? 2
 denote the mean and variance of the correct observations respectively, 
then 15( ?? + ?? 2
+ ?? 2
) is equal to 
Q5 - 2024 (29 Jan Shift 1) 
If the mean and variance of the data 65,68,58,44,48,45,60, ?? , ?? , 60 where ?? > ?? are 56 
and 66.2 respectively, then ?? 2
+ ?? 2
 is equal to 
Q6 - 2024 (29 Jan Shift 2) 
If the mean and variance of five observations are 
24
5
 and 
194
25
 respectively and the mean of 
first four observations is 
7
2
, then the variance of the first four observations in equal to 
(1) 
4
5
 
(2) 
77
12
 
(3) 
5
4
 
(4) 
105
4
 
Q7 - 2024 (30 Jan Shift 1) 
Let ?? denote the median of the following frequency distribution. 
Class 0 - 4 4 - 8 8 - 12 12 - 16 16 - 20 
Frequency 3 9 10 8 6 
 
Then 20M is equal to : 
(1) 416 
(2) 104 
(3) 52 
(4) 208 
The variance ?? 2
 of the data 
?? ?? 0 1 5 6 10 12 17 
?? ?? 3 2 3 2 6 3 3 
 
Is 
Q9 - 2024 (31 Jan Shift 2) 
Let the mean and the variance of 6 observation a, b, 68,44,48,60 be 55 and 194 , 
respectively if ?? > ?? , then ?? + 3?? is 
(1) 200 
(2) 190 
(3) 180 
(4) 210 
Answer Key 
Q1 (3)  ???? (1) Q3 (2) Q4 (2521) 
Q5 (6344) Q6 (3) Q7 (4) Q8 (29) 
Q9 (3)    
 
Solutions 
Q1 
 Median = 170 ? 125 , a, b, 170,190,210,230 
Mean deviation about 
Median = 
0 + 45 + 60 + 20 + 40 + 170 - ?? + 170 - ?? 7
=
205
7
 
? a + b = 300 
Mean =
170+125+230+190+210+?? +?? 7
= 175 
Mean deviation 
About mean = 
50 + 175 - ?? + 175 - ?? + 5 + 15 + 35 + 55
7
= 30 
Q2 
x
1
, x
2
… … x
10
 
?
i=1
10
?( x
i
- ?? )= 2 ? ?
i=1
10
?x
i
- 10?? = 2 
Mean ?? =
6
5
=
?x
i
10
 
? ?x
i
= 12 
10?? + 2 = 12 ? ?? = 1 
Now ?
i=1
10
?( x
i
- ?? )
2
= 40  Let y
i
= x
i
- ?? 
? ?? y
2
=
1
10
?y
i
2
- ( y ¯)
2
 
?? ?? 2
=
1
10
?( ?? ?? - ?? )
2
- (
?
?? =1
10
?( ?? ?? - ?? )
10
)
2
 
84
25
= 4 - (
12 - 10?? 10
)
2
 
? (
6 - 5?? 5
)
2
= 4 -
84
25
=
16
25
 
6 - 5?? = ±4 ? ?? =
2
5
 (not possible) or ?? = 2 
Hence 
?? ?? = 2 
Q3 
?
k=1
10
?a
k
= 50 
?? 1
+ ?? 2
+ ? + ?? 10
= 50… 
?
?k<j
?a
k
a
j
= 1100. 
If a
1
+ a
2
+ ? + a
10
= 50. 
( ?? 1
+ ?? 2
+ ? + ?? 10
)
2
= 2500 
Page 5


JEE Mains Previous Year Questions 
(2021-2024): Statistics 
2024 
Q1 - 2024 (01 Feb Shift 1) 
Let the median and the mean deviation about the median of 7 observation 
170,125,230,190,210, a, b be 170 and 
205
7
 respectively. Then the mean deviation about 
the mean of these 7 observations is : 
(1) 31 
(2) 28 
(3) 30 
(4) 32 
Q2 - 2024 (01 Feb Shift 2) 
Consider 10 observationx
1
, ?? 2,…
, ?? 10
. such that ?
?? =1
10
?( ?? ?? - ?? )= 2 and ?
?? =1
10
?( ?? ?? - ?? )
2
= 40, 
where ?? , ?? are positive integers. Let the mean and the variance of the observations be 
6
5
 
and 
84
25
 respectively. The 
?? ?? is equal to : 
(1) 2 
(2) 
3
2
 
(3) 
5
2
 
(4) 1 
Q3 - 2024 (27 Jan Shift 1) 
Let ?? 1
, ?? 2
, … ?? 10
 be 10 observations such that ?
k=1
10
?a
k
= 50 and ?
?k<j
?a
k
· a
j
= 1100. Then 
the standard deviation of ?? 1
, ?? 2
, … , ?? 10
 is equal to : 
(1) 5 
(2) v 5 
(3) 10 
(4) v 115 
Q4 - 2024 (27 Jan Shift 2) 
The mean and standard deviation of 15 observations were found to be 12 and 3 
respectively. On rechecking it was found that an observation was read as 10 in place of 
12 . If ?? and ?? 2
 denote the mean and variance of the correct observations respectively, 
then 15( ?? + ?? 2
+ ?? 2
) is equal to 
Q5 - 2024 (29 Jan Shift 1) 
If the mean and variance of the data 65,68,58,44,48,45,60, ?? , ?? , 60 where ?? > ?? are 56 
and 66.2 respectively, then ?? 2
+ ?? 2
 is equal to 
Q6 - 2024 (29 Jan Shift 2) 
If the mean and variance of five observations are 
24
5
 and 
194
25
 respectively and the mean of 
first four observations is 
7
2
, then the variance of the first four observations in equal to 
(1) 
4
5
 
(2) 
77
12
 
(3) 
5
4
 
(4) 
105
4
 
Q7 - 2024 (30 Jan Shift 1) 
Let ?? denote the median of the following frequency distribution. 
Class 0 - 4 4 - 8 8 - 12 12 - 16 16 - 20 
Frequency 3 9 10 8 6 
 
Then 20M is equal to : 
(1) 416 
(2) 104 
(3) 52 
(4) 208 
The variance ?? 2
 of the data 
?? ?? 0 1 5 6 10 12 17 
?? ?? 3 2 3 2 6 3 3 
 
Is 
Q9 - 2024 (31 Jan Shift 2) 
Let the mean and the variance of 6 observation a, b, 68,44,48,60 be 55 and 194 , 
respectively if ?? > ?? , then ?? + 3?? is 
(1) 200 
(2) 190 
(3) 180 
(4) 210 
Answer Key 
Q1 (3)  ???? (1) Q3 (2) Q4 (2521) 
Q5 (6344) Q6 (3) Q7 (4) Q8 (29) 
Q9 (3)    
 
Solutions 
Q1 
 Median = 170 ? 125 , a, b, 170,190,210,230 
Mean deviation about 
Median = 
0 + 45 + 60 + 20 + 40 + 170 - ?? + 170 - ?? 7
=
205
7
 
? a + b = 300 
Mean =
170+125+230+190+210+?? +?? 7
= 175 
Mean deviation 
About mean = 
50 + 175 - ?? + 175 - ?? + 5 + 15 + 35 + 55
7
= 30 
Q2 
x
1
, x
2
… … x
10
 
?
i=1
10
?( x
i
- ?? )= 2 ? ?
i=1
10
?x
i
- 10?? = 2 
Mean ?? =
6
5
=
?x
i
10
 
? ?x
i
= 12 
10?? + 2 = 12 ? ?? = 1 
Now ?
i=1
10
?( x
i
- ?? )
2
= 40  Let y
i
= x
i
- ?? 
? ?? y
2
=
1
10
?y
i
2
- ( y ¯)
2
 
?? ?? 2
=
1
10
?( ?? ?? - ?? )
2
- (
?
?? =1
10
?( ?? ?? - ?? )
10
)
2
 
84
25
= 4 - (
12 - 10?? 10
)
2
 
? (
6 - 5?? 5
)
2
= 4 -
84
25
=
16
25
 
6 - 5?? = ±4 ? ?? =
2
5
 (not possible) or ?? = 2 
Hence 
?? ?? = 2 
Q3 
?
k=1
10
?a
k
= 50 
?? 1
+ ?? 2
+ ? + ?? 10
= 50… 
?
?k<j
?a
k
a
j
= 1100. 
If a
1
+ a
2
+ ? + a
10
= 50. 
( ?? 1
+ ?? 2
+ ? + ?? 10
)
2
= 2500 
? ?
i=1
10
?a
i
2
+ 2?
k<j
?a
k
a
j
= 2500 
? ?
i=1
10
?a
i
2
= 2500 - 2( 1100 ) 
?
i=1
10
?a
i
2
= 300, Standard deviation ' ?? ' 
=
v
?a
i
2
10
- (
?a
i
10
)
2
=
v
300
10
- (
50
10
)
2
 
= v 30 - 25 = v 5 
Q4 
Let the incorrect mean be ?? '
 and standard deviation be ?? '
 
We have 
?? '
=
Sx
i
15
= 12 ? Sx
i
= 180 
As per given information correct Sx
i
= 180 - 10 + 12 
? ?? ( correct mean )=
182
15
 
Also 
?? '
=
v
Sx
i
 
2
15
- 144 = 3 ? Sx
i
 
2
= 2295 
Correct Sx
i
 
2
= 2295 - 100 + 144 = 2339 
?? 2
( correct variance )=
2339
15
-
182×182
15×15
 
Required value 
 = 15( ?? + ?? 2
+ ?? 2
)
 = 15(
182
15
+
182 × 182
15 × 15
+
2339
15
-
182 × 182
15 × 15
)
 = 15(
182
15
+
2339
15
)
 = 2521 
 
Q5 
x ¯ = 56 
?? 2
= 66.2
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FAQs on Statistics: JEE Mains Previous Year Questions (2021-2024) - Mathematics (Maths) for JEE Main & Advanced

1. What are some important topics to focus on in Statistics for JEE Mains?
Ans. Some important topics to focus on in Statistics for JEE Mains include Measures of Central Tendency, Measures of Dispersion, Probability, Random Variables, and Distribution Functions.
2. How can I improve my understanding of Statistics for JEE Mains?
Ans. To improve your understanding of Statistics for JEE Mains, you can practice solving a variety of problems, refer to standard textbooks, take online quizzes and mock tests, and seek help from teachers or tutors if needed.
3. Are there any specific tips for scoring well in the Statistics section of JEE Mains?
Ans. Some tips for scoring well in the Statistics section of JEE Mains include understanding the concepts thoroughly, practicing regularly, managing time effectively during the exam, and focusing on solving previous year question papers.
4. How important is Statistics in the JEE Mains exam?
Ans. Statistics is an important subject in the JEE Mains exam as it carries weightage in the Mathematics section. A good understanding of Statistics can help improve overall scores in the exam.
5. Can you recommend any online resources for studying Statistics for JEE Mains?
Ans. Some online resources for studying Statistics for JEE Mains include Khan Academy, Coursera, edX, and various YouTube channels dedicated to JEE preparation. These platforms offer video lectures, practice problems, and mock tests to help students prepare effectively.
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