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Joint Entrance Examination
Mathematics
Statistics
Question 141
Question 141 of 208
Medium
MCQ
If the data
x
1
,
x
2
,
…
,
x
10
x_1,x_2,\ldots,x_{10}
x
1
,
x
2
,
…
,
x
10
is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2,000; then the standard deviation of this data is:
A
2
2
2\sqrt{2}
2
2
B
2
C
4
D
2
\sqrt{2}
2
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Official solution
x
1
+
x
2
+
x
3
+
x
4
=
44
x_1+x_2+x_3+x_4=44
x
1
+
x
2
+
x
3
+
x
4
=
44
;
x
5
+
⋯
+
x
10
=
96
x_5+\cdots+x_{10}=96
x
5
+
⋯
+
x
10
=
96
;
∑
x
i
2
=
2000
\sum x_i^2=2000
∑
x
i
2
=
2000
\[\sigma^2 = \frac{2000}{10}-\left(\frac{44+96}{10}\right)^2 = 200-196=4 \implies \sigma=2\]
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