Find the Variance 22 , 15 , 69 , 65 , 85 , 74 , 45 , 45 , 45 , 22

Math
22 , 15 , 69 , 65 , 85 , 74 , 45 , 45 , 45 , 22
The mean of a set of numbers is the sum divided by the number of terms.
x‾=22+15+69+65+85+74+45+45+45+2210
Simplify the numerator.
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Add 22 and 15.
x‾=37+69+65+85+74+45+45+45+2210
Add 37 and 69.
x‾=106+65+85+74+45+45+45+2210
Add 106 and 65.
x‾=171+85+74+45+45+45+2210
Add 171 and 85.
x‾=256+74+45+45+45+2210
Add 256 and 74.
x‾=330+45+45+45+2210
Add 330 and 45.
x‾=375+45+45+2210
Add 375 and 45.
x‾=420+45+2210
Add 420 and 45.
x‾=465+2210
Add 465 and 22.
x‾=48710
x‾=48710
Divide.
x‾=48.7
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=(22-48.7)2+(15-48.7)2+(69-48.7)2+(65-48.7)2+(85-48.7)2+(74-48.7)2+(45-48.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Simplify the result.
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Simplify the numerator.
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Subtract 48.7 from 22.
s=(-26.7)2+(15-48.7)2+(69-48.7)2+(65-48.7)2+(85-48.7)2+(74-48.7)2+(45-48.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Raise -26.7 to the power of 2.
s=712.89+(15-48.7)2+(69-48.7)2+(65-48.7)2+(85-48.7)2+(74-48.7)2+(45-48.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Subtract 48.7 from 15.
s=712.89+(-33.7)2+(69-48.7)2+(65-48.7)2+(85-48.7)2+(74-48.7)2+(45-48.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Raise -33.7 to the power of 2.
s=712.89+1135.69+(69-48.7)2+(65-48.7)2+(85-48.7)2+(74-48.7)2+(45-48.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Subtract 48.7 from 69.
s=712.89+1135.69+20.32+(65-48.7)2+(85-48.7)2+(74-48.7)2+(45-48.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Raise 20.3 to the power of 2.
s=712.89+1135.69+412.09+(65-48.7)2+(85-48.7)2+(74-48.7)2+(45-48.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Subtract 48.7 from 65.
s=712.89+1135.69+412.09+16.32+(85-48.7)2+(74-48.7)2+(45-48.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Raise 16.3 to the power of 2.
s=712.89+1135.69+412.09+265.69+(85-48.7)2+(74-48.7)2+(45-48.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Subtract 48.7 from 85.
s=712.89+1135.69+412.09+265.69+36.32+(74-48.7)2+(45-48.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Raise 36.3 to the power of 2.
s=712.89+1135.69+412.09+265.69+1317.69+(74-48.7)2+(45-48.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Subtract 48.7 from 74.
s=712.89+1135.69+412.09+265.69+1317.69+25.32+(45-48.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Raise 25.3 to the power of 2.
s=712.89+1135.69+412.09+265.69+1317.69+640.09+(45-48.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Subtract 48.7 from 45.
s=712.89+1135.69+412.09+265.69+1317.69+640.09+(-3.7)2+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Raise -3.7 to the power of 2.
s=712.89+1135.69+412.09+265.69+1317.69+640.09+13.69+(45-48.7)2+(45-48.7)2+(22-48.7)210-1
Subtract 48.7 from 45.
s=712.89+1135.69+412.09+265.69+1317.69+640.09+13.69+(-3.7)2+(45-48.7)2+(22-48.7)210-1
Raise -3.7 to the power of 2.
s=712.89+1135.69+412.09+265.69+1317.69+640.09+13.69+13.69+(45-48.7)2+(22-48.7)210-1
Subtract 48.7 from 45.
s=712.89+1135.69+412.09+265.69+1317.69+640.09+13.69+13.69+(-3.7)2+(22-48.7)210-1
Raise -3.7 to the power of 2.
s=712.89+1135.69+412.09+265.69+1317.69+640.09+13.69+13.69+13.69+(22-48.7)210-1
Subtract 48.7 from 22.
s=712.89+1135.69+412.09+265.69+1317.69+640.09+13.69+13.69+13.69+(-26.7)210-1
Raise -26.7 to the power of 2.
s=712.89+1135.69+412.09+265.69+1317.69+640.09+13.69+13.69+13.69+712.8910-1
Add 712.89 and 1135.69.
s=1848.58+412.09+265.69+1317.69+640.09+13.69+13.69+13.69+712.8910-1
Add 1848.58 and 412.09.
s=2260.67+265.69+1317.69+640.09+13.69+13.69+13.69+712.8910-1
Add 2260.67 and 265.69.
s=2526.36+1317.69+640.09+13.69+13.69+13.69+712.8910-1
Add 2526.36 and 1317.69.
s=3844.05+640.09+13.69+13.69+13.69+712.8910-1
Add 3844.05 and 640.09.
s=4484.14+13.69+13.69+13.69+712.8910-1
Add 4484.14 and 13.69.
s=4497.83+13.69+13.69+712.8910-1
Add 4497.83 and 13.69.
s=4511.52+13.69+712.8910-1
Add 4511.52 and 13.69.
s=4525.21+712.8910-1
Add 4525.21 and 712.89.
s=5238.110-1
s=5238.110-1
Simplify the expression.
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Subtract 1 from 10.
s=5238.19
Divide 5238.1 by 9.
s=582.01‾
s=582.01‾
s=582.01‾
Approximate the result.
s2≈582.0111
Find the Variance 22 , 15 , 69 , 65 , 85 , 74 , 45 , 45 , 45 , 22

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