Find the Variance 23 , 4 , 19 , 21 , 17 , 26 , 29 , 17 , 6

Math
23 , 4 , 19 , 21 , 17 , 26 , 29 , 17 , 6
The mean of a set of numbers is the sum divided by the number of terms.
x‾=23+4+19+21+17+26+29+17+69
Simplify the numerator.
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Add 23 and 4.
x‾=27+19+21+17+26+29+17+69
Add 27 and 19.
x‾=46+21+17+26+29+17+69
Add 46 and 21.
x‾=67+17+26+29+17+69
Add 67 and 17.
x‾=84+26+29+17+69
Add 84 and 26.
x‾=110+29+17+69
Add 110 and 29.
x‾=139+17+69
Add 139 and 17.
x‾=156+69
Add 156 and 6.
x‾=1629
x‾=1629
Divide 162 by 9.
x‾=18
Set up the formula for variance. The variance of a set of values is a measure of the spread of its values.
s2=∑i=1n⁡(xi-xavg)2n-1
Set up the formula for variance for this set of numbers.
s=(23-18)2+(4-18)2+(19-18)2+(21-18)2+(17-18)2+(26-18)2+(29-18)2+(17-18)2+(6-18)29-1
Simplify the result.
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Simplify the numerator.
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Subtract 18 from 23.
s=52+(4-18)2+(19-18)2+(21-18)2+(17-18)2+(26-18)2+(29-18)2+(17-18)2+(6-18)29-1
Raise 5 to the power of 2.
s=25+(4-18)2+(19-18)2+(21-18)2+(17-18)2+(26-18)2+(29-18)2+(17-18)2+(6-18)29-1
Subtract 18 from 4.
s=25+(-14)2+(19-18)2+(21-18)2+(17-18)2+(26-18)2+(29-18)2+(17-18)2+(6-18)29-1
Raise -14 to the power of 2.
s=25+196+(19-18)2+(21-18)2+(17-18)2+(26-18)2+(29-18)2+(17-18)2+(6-18)29-1
Subtract 18 from 19.
s=25+196+12+(21-18)2+(17-18)2+(26-18)2+(29-18)2+(17-18)2+(6-18)29-1
One to any power is one.
s=25+196+1+(21-18)2+(17-18)2+(26-18)2+(29-18)2+(17-18)2+(6-18)29-1
Subtract 18 from 21.
s=25+196+1+32+(17-18)2+(26-18)2+(29-18)2+(17-18)2+(6-18)29-1
Raise 3 to the power of 2.
s=25+196+1+9+(17-18)2+(26-18)2+(29-18)2+(17-18)2+(6-18)29-1
Subtract 18 from 17.
s=25+196+1+9+(-1)2+(26-18)2+(29-18)2+(17-18)2+(6-18)29-1
Raise -1 to the power of 2.
s=25+196+1+9+1+(26-18)2+(29-18)2+(17-18)2+(6-18)29-1
Subtract 18 from 26.
s=25+196+1+9+1+82+(29-18)2+(17-18)2+(6-18)29-1
Raise 8 to the power of 2.
s=25+196+1+9+1+64+(29-18)2+(17-18)2+(6-18)29-1
Subtract 18 from 29.
s=25+196+1+9+1+64+112+(17-18)2+(6-18)29-1
Raise 11 to the power of 2.
s=25+196+1+9+1+64+121+(17-18)2+(6-18)29-1
Subtract 18 from 17.
s=25+196+1+9+1+64+121+(-1)2+(6-18)29-1
Raise -1 to the power of 2.
s=25+196+1+9+1+64+121+1+(6-18)29-1
Subtract 18 from 6.
s=25+196+1+9+1+64+121+1+(-12)29-1
Raise -12 to the power of 2.
s=25+196+1+9+1+64+121+1+1449-1
Add 25 and 196.
s=221+1+9+1+64+121+1+1449-1
Add 221 and 1.
s=222+9+1+64+121+1+1449-1
Add 222 and 9.
s=231+1+64+121+1+1449-1
Add 231 and 1.
s=232+64+121+1+1449-1
Add 232 and 64.
s=296+121+1+1449-1
Add 296 and 121.
s=417+1+1449-1
Add 417 and 1.
s=418+1449-1
Add 418 and 144.
s=5629-1
s=5629-1
Reduce the expression by cancelling the common factors.
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Subtract 1 from 9.
s=5628
Cancel the common factor of 562 and 8.
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Factor 2 out of 562.
s=2(281)8
Cancel the common factors.
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Factor 2 out of 8.
s=2⋅2812⋅4
Cancel the common factor.
s=2⋅2812⋅4
Rewrite the expression.
s=2814
s=2814
s=2814
s=2814
s=2814
Approximate the result.
s2≈70.25
Find the Variance 23 , 4 , 19 , 21 , 17 , 26 , 29 , 17 , 6

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