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Byju's Answer
Standard XI
Statistics
Direct Method
If a variable...
Question
If a variable X takes values 0, 1, 2,..., n with frequencies
n
C
0
,
n
C
1
,
n
C
2
, ... ,
n
C
n
, then write variance X.
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Solution
x
=
∑
i
=
0
n
x
i
f
i
∑
i
=
0
n
f
i
=
0
×
C
o
n
+
1
×
C
1
n
+
.
.
.
+
n
×
C
n
n
C
o
n
+
C
1
n
+
.
.
.
+
C
n
n
⇒
x
=
n
×
2
n
-
1
2
n
n
+
1
=
n
n
+
1
2
∴
V
a
r
(
X
)
=
σ
2
=
1
n
∑
i
=
0
n
x
i
-
x
2
=
1
n
0
+
1
+
2
+
.
.
.
.
+
n
-
n
x
2
⇒
σ
2
=
1
n
n
n
+
1
2
-
n
×
n
n
+
1
2
2
=
1
n
n
n
+
1
2
1
-
n
2
=
n
2
4
n
n
+
1
2
n
-
1
2
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0
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Q.
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