Find the Variance 15 , 32 , 25 , 16 , 10

Math
15 , 32 , 25 , 16 , 10
The mean of a set of numbers is the sum divided by the number of terms.
x‾=15+32+25+16+105
Simplify the numerator.
Tap for more steps…
Add 15 and 32.
x‾=47+25+16+105
Add 47 and 25.
x‾=72+16+105
Add 72 and 16.
x‾=88+105
Add 88 and 10.
x‾=985
x‾=985
Divide.
x‾=19.6
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=(15-19.6)2+(32-19.6)2+(25-19.6)2+(16-19.6)2+(10-19.6)25-1
Simplify the result.
Tap for more steps…
Simplify the numerator.
Tap for more steps…
Subtract 19.6 from 15.
s=(-4.6)2+(32-19.6)2+(25-19.6)2+(16-19.6)2+(10-19.6)25-1
Raise -4.6 to the power of 2.
s=21.16+(32-19.6)2+(25-19.6)2+(16-19.6)2+(10-19.6)25-1
Subtract 19.6 from 32.
s=21.16+12.42+(25-19.6)2+(16-19.6)2+(10-19.6)25-1
Raise 12.4 to the power of 2.
s=21.16+153.76+(25-19.6)2+(16-19.6)2+(10-19.6)25-1
Subtract 19.6 from 25.
s=21.16+153.76+5.42+(16-19.6)2+(10-19.6)25-1
Raise 5.4 to the power of 2.
s=21.16+153.76+29.16+(16-19.6)2+(10-19.6)25-1
Subtract 19.6 from 16.
s=21.16+153.76+29.16+(-3.6)2+(10-19.6)25-1
Raise -3.6 to the power of 2.
s=21.16+153.76+29.16+12.96+(10-19.6)25-1
Subtract 19.6 from 10.
s=21.16+153.76+29.16+12.96+(-9.6)25-1
Raise -9.6 to the power of 2.
s=21.16+153.76+29.16+12.96+92.165-1
Add 21.16 and 153.76.
s=174.92+29.16+12.96+92.165-1
Add 174.92 and 29.16.
s=204.08+12.96+92.165-1
Add 204.08 and 12.96.
s=217.04+92.165-1
Add 217.04 and 92.16.
s=309.25-1
s=309.25-1
Simplify the expression.
Tap for more steps…
Subtract 1 from 5.
s=309.24
Divide 309.2 by 4.
s=77.3
s=77.3
s=77.3
Approximate the result.
s2≈77.3
Find the Variance 15 , 32 , 25 , 16 , 10

Solving MATH problems

We can solve all math problems. Get help on the web or with our math app

Scroll to top