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JEE Main 6 Apr 2024 Shift 1 Solved Paper
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© examsnet.com
Question : 4
Total: 89
The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On respectively, it was found that an observation by mistake was taken 8 instead of 12 . The correct standard deviation is
[6 Apr 2024 Shift 1]
√
3.86
1.8
√
3.96
1.94
Validate
Solution:
👈: Video Solution
Mean
(
x
)
=
10
⇒
Σ
x
i
20
=
10
Σ
x
i
=
10
×
20
=
200
If 8 is replaced by 12 , then
Σ
x
1
=
200
−
8
+
12
=
204
∴
Correct mean
(
x
)
=
Σ
x
i
20
=
204
20
=
10.2
∵
Standard deviation
=
2
∴
Variance
=
(
S.D.
)
2
=
2
2
=
4
⇒
Σ
x
i
2
20
−
(
Σ
x
i
20
)
2
=
4
⇒
Σ
x
i
2
20
−
(
10
)
2
=
4
⇒
Σ
x
i
2
20
=
104
⇒
Σ
x
i
2
=
2080
Now, replaced ' 8 ' observations by ' 12 '
Then,
Σ
x
i
2
=
2080
−
8
2
+
12
2
=
2160
∴
Variance of removing observations
⇒
Σ
x
i
2
20
−
(
Σ
x
i
20
)
2
⇒
2160
20
−
(
10.2
)
2
⇒
108
−
104.04
⇒
3.96
Correct standard deviation
=
√
3.96
© examsnet.com
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