Page 1
JEE Mains Previous Year Questions
(20212024): 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
(20212024): 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
(20212024): 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
(20212024): 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
(20212024): 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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