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JEE Main Math Class 12 Statistics Part 2 Questions
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Question : 9
Total: 28
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
µ
and
σ
2
denote the mean and variance of the correct observations respectively, then
15
(
µ
+
µ
2
+
σ
2
)
is equal to___
[27-Jan-2024 Shift 2]
Your Answer:
Validate
Solution:
👈: Video Solution
Let the incorrect mean be
µ
′
and standard deviation be
σ
′
We have
µ
′
=
Σ
x
i
15
=
12
⇒
Σ
x
i
=
180
As per given information correct
Σ
x
i
=
180
−
10
+
12
⇒
µ
(
correct mean
)
=
182
15
Also
σ
′
=
√
Σ
x
i
2
15
−
144
=
3
⇒
Σ
x
i
2
=
2295
Correct
Σ
x
i
2
=
2295
−
100
+
144
=
2339
σ
2
(
correct variance
)
=
2339
15
−
182
×
182
15
×
15
Required value
=
15
(
µ
+
µ
2
+
σ
2
)
=
15
(
182
15
+
182
×
182
15
×
15
+
2339
15
−
182
×
182
15
×
15
)
=
15
(
182
15
+
2339
15
)
=
2521
© examsnet.com
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