Answer:
The complete question is attached.
To find the variance and deviation, we have to use their definition or formulas:
Standard deviation.
[tex]\sigma=\sqrt{\frac{\sum (x- \mu)^{2} }{N}}[/tex]
So, first we have to find the difference between each number and the mean:
76-81=-5
87-81=6
65-81=-16
88-81=7
67-81=-14
84-81=3
77-81=-4
82-81=1
91-81=10
85-81=4
90-81=9
Now, we have to elevate each difference to the squared power and then sum all:
[tex]25+36+256+49+196+9+16+1+100+16+81=785[/tex]
Then, we replace in the formula:
[tex]\sigma=\sqrt{\frac{785}{11}} \approx 8.45[/tex]
Variance.
The variance is just the squared power of the standard deviation. So:
[tex]\sigma^{2}=(8.45)^{2}=71.40[/tex]
