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Find the Variance 21 , 12 , 6 , 7 , 9
21
,
12
,
6
,
7
,
9
Step 1
The
mean
of a
set
of numbers is the
sum
divided by the number of
terms
.
‾
x
=
21
+
12
+
6
+
7
+
9
5
Step 2
Simplify the
numerator
.
Add
21
and
12
.
‾
x
=
33
+
6
+
7
+
9
5
Add
33
and
6
.
‾
x
=
39
+
7
+
9
5
Add
39
and
7
.
‾
x
=
46
+
9
5
Add
46
and
9
.
‾
x
=
55
5
‾
x
=
55
5
Step 3
Divide
55
by
5
.
‾
x
=
11
Step 4
Set
up the
formula
for variance. The variance of a
set
of values is a
measure
of the spread of its values.
s
2
=
n
∑
i
=
1
(
x
i
-
x
a
v
g
)
2
n
-
1
Step 5
Set
up the
formula
for variance for this
set
of numbers.
s
=
(
21
-
11
)
2
+
(
12
-
11
)
2
+
(
6
-
11
)
2
+
(
7
-
11
)
2
+
(
9
-
11
)
2
5
-
1
Step 6
Simplify the result.
Simplify the
numerator
.
Subtract
11
from
21
.
s
=
10
2
+
(
12
-
11
)
2
+
(
6
-
11
)
2
+
(
7
-
11
)
2
+
(
9
-
11
)
2
5
-
1
Raise
10
to the
power
of
2
.
s
=
100
+
(
12
-
11
)
2
+
(
6
-
11
)
2
+
(
7
-
11
)
2
+
(
9
-
11
)
2
5
-
1
Subtract
11
from
12
.
s
=
100
+
1
2
+
(
6
-
11
)
2
+
(
7
-
11
)
2
+
(
9
-
11
)
2
5
-
1
One to any
power
is one.
s
=
100
+
1
+
(
6
-
11
)
2
+
(
7
-
11
)
2
+
(
9
-
11
)
2
5
-
1
Subtract
11
from
6
.
s
=
100
+
1
+
(
-
5
)
2
+
(
7
-
11
)
2
+
(
9
-
11
)
2
5
-
1
Raise
-
5
to the
power
of
2
.
s
=
100
+
1
+
25
+
(
7
-
11
)
2
+
(
9
-
11
)
2
5
-
1
Subtract
11
from
7
.
s
=
100
+
1
+
25
+
(
-
4
)
2
+
(
9
-
11
)
2
5
-
1
Raise
-
4
to the
power
of
2
.
s
=
100
+
1
+
25
+
16
+
(
9
-
11
)
2
5
-
1
Subtract
11
from
9
.
s
=
100
+
1
+
25
+
16
+
(
-
2
)
2
5
-
1
Raise
-
2
to the
power
of
2
.
s
=
100
+
1
+
25
+
16
+
4
5
-
1
Add
100
and
1
.
s
=
101
+
25
+
16
+
4
5
-
1
Add
101
and
25
.
s
=
126
+
16
+
4
5
-
1
Add
126
and
16
.
s
=
142
+
4
5
-
1
Add
142
and
4
.
s
=
146
5
-
1
s
=
146
5
-
1
Reduce the
expression
by cancelling the
common factors
.
Subtract
1
from
5
.
s
=
146
4
Cancel the
common factor
of
146
and
4
.
Factor
2
out of
146
.
s
=
2
(
73
)
4
Cancel the
common factors
.
Factor
2
out of
4
.
s
=
2
⋅
73
2
⋅
2
Cancel the
common factor
.
s
=
2
⋅
73
2
⋅
2
Rewrite the
expression
.
s
=
73
2
s
=
73
2
s
=
73
2
s
=
73
2
s
=
73
2
Step 7
Approximate
the result.
s
2
≈
36.5
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