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JEE Main Math Class 12 Statistics Part 2 Questions
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Question : 27
Total: 28
The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively, Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is _______.
[13-Apr-2023 shift 2]
Your Answer:
Validate
Solution:
Mean
=
Σ
x
i
10
⇒
50
=
Σ
x
i
10
⇒
Σ
x
i
=
500
correct
∑
x
i
=
500
−
45
−
50
+
20
+
25
=
450
σ
2
=
Σ
x
i
2
10
=
(
x
)
2
⇒
144
=
Σ
x
i
2
10
−
2500
⇒
Σ
x
i
2
=
26440
correct
∑
x
i
2
=
26440
−
(
45
)
2
−
(
50
)
2
+
(
20
)
2
+
(
25
)
2
=
26440
−
2025
−
2500
+
400
+
625
=
22940
σ
2
=
correct
Σ
x
i
2
10
−
(
correct
Σ
x
i
10
)
2
=
22940
10
−
(
450
10
)
2
=
2294
−
2025
=
269
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