Statistics Examples

1414 , 1717 , 2121 , 4444 , 7979
Step 1
The mean of a set of numbers is the sum divided by the number of terms.
x=14+17+21+44+795¯x=14+17+21+44+795
Step 2
Simplify the numerator.
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Step 2.1
Add 1414 and 1717.
x=31+21+44+795¯x=31+21+44+795
Step 2.2
Add 3131 and 2121.
x=52+44+795¯x=52+44+795
Step 2.3
Add 5252 and 4444.
x=96+795¯x=96+795
Step 2.4
Add 9696 and 7979.
x=1755¯x=1755
x=1755¯x=1755
Step 3
Divide 175175 by 55.
x=35¯x=35
Step 4
Set up the formula for variance. The variance of a set of values is a measure of the spread of its values.
s2=ni=1(xi-xavg)2n-1s2=ni=1(xixavg)2n1
Step 5
Set up the formula for variance for this set of numbers.
s=(14-35)2+(17-35)2+(21-35)2+(44-35)2+(79-35)25-1s=(1435)2+(1735)2+(2135)2+(4435)2+(7935)251
Step 6
Simplify the result.
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Step 6.1
Simplify the numerator.
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Step 6.1.1
Subtract 3535 from 1414.
s=(-21)2+(17-35)2+(21-35)2+(44-35)2+(79-35)25-1s=(21)2+(1735)2+(2135)2+(4435)2+(7935)251
Step 6.1.2
Raise -2121 to the power of 22.
s=441+(17-35)2+(21-35)2+(44-35)2+(79-35)25-1s=441+(1735)2+(2135)2+(4435)2+(7935)251
Step 6.1.3
Subtract 3535 from 1717.
s=441+(-18)2+(21-35)2+(44-35)2+(79-35)25-1s=441+(18)2+(2135)2+(4435)2+(7935)251
Step 6.1.4
Raise -1818 to the power of 22.
s=441+324+(21-35)2+(44-35)2+(79-35)25-1s=441+324+(2135)2+(4435)2+(7935)251
Step 6.1.5
Subtract 3535 from 2121.
s=441+324+(-14)2+(44-35)2+(79-35)25-1s=441+324+(14)2+(4435)2+(7935)251
Step 6.1.6
Raise -1414 to the power of 22.
s=441+324+196+(44-35)2+(79-35)25-1s=441+324+196+(4435)2+(7935)251
Step 6.1.7
Subtract 3535 from 4444.
s=441+324+196+92+(79-35)25-1s=441+324+196+92+(7935)251
Step 6.1.8
Raise 99 to the power of 22.
s=441+324+196+81+(79-35)25-1s=441+324+196+81+(7935)251
Step 6.1.9
Subtract 3535 from 7979.
s=441+324+196+81+4425-1s=441+324+196+81+44251
Step 6.1.10
Raise 4444 to the power of 22.
s=441+324+196+81+19365-1s=441+324+196+81+193651
Step 6.1.11
Add 441441 and 324324.
s=765+196+81+19365-1s=765+196+81+193651
Step 6.1.12
Add 765765 and 196196.
s=961+81+19365-1s=961+81+193651
Step 6.1.13
Add 961961 and 8181.
s=1042+19365-1s=1042+193651
Step 6.1.14
Add 10421042 and 19361936.
s=29785-1s=297851
s=29785-1s=297851
Step 6.2
Reduce the expression by cancelling the common factors.
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Step 6.2.1
Subtract 11 from 55.
s=29784s=29784
Step 6.2.2
Cancel the common factor of 29782978 and 44.
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Step 6.2.2.1
Factor 22 out of 29782978.
s=2(1489)4s=2(1489)4
Step 6.2.2.2
Cancel the common factors.
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Step 6.2.2.2.1
Factor 22 out of 44.
s=2148922s=2148922
Step 6.2.2.2.2
Cancel the common factor.
s=2148922
Step 6.2.2.2.3
Rewrite the expression.
s=14892
s=14892
s=14892
s=14892
s=14892
Step 7
Approximate the result.
s2744.5
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 [x2  12  π  xdx ] 
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