Question

Adimas found the mean of her 11 math test scores for the first semester.

Answer 1

Answer: O^2= 71.36

               O=8.45  

Answer 2

Answer:

The complete question is attached.

To find the variance and deviation, we have to use their definition or formulas:

Standard deviation.

$\sigma=\sqrt{\frac{\sum (x- \mu)^{2} }{N}}$

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:

$25+36+256+49+196+9+16+1+100+16+81=785$

Then, we replace in the formula:

$\sigma=\sqrt{\frac{785}{11}} \approx 8.45$

Variance.

The variance is just the squared power of the standard deviation. So:

$\sigma^{2}=(8.45)^{2}=71.40$