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Standard XI
Mathematics
NCERT
Question
Find the mean and variance for the data
X
i
6
10
14
18
24
28
30
f
i
2
4
7
12
8
4
3
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Solution
Verified by Toppr
The data is obtained in tabular form as follows
X
i
f
i
f
i
X
i
X
i
−
¯
X
(
X
i
−
¯
X
)
2
f
i
(
X
i
−
¯
X
)
2
6
2
12
-13
169
338
10
4
40
-9
81
324
14
7
98
-5
25
175
18
12
216
-1
1
12
24
8
192
5
25
200
28
4
112
9
81
324
30
3
90
11
121
363
40
760
1736
Here,
N
=
40
,
7
∑
i
=
1
f
i
x
i
=
760
∴
¯
x
=
∑
7
i
=
1
f
i
x
i
N
=
760
40
=
19
and Variance
(
σ
2
)
=
1
N
7
∑
i
=
1
f
i
(
x
i
−
¯
X
)
2
=
1
40
×
1736
=
43.4
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