To find the solution we will first find the difference between each number and mean, and then substitute the value in the formula of standard deviation.

The standard deviation is 8.4477 and the variance is 71.40.

Given to us

Test scores of Adimas = (76, 87, 65, 88, 67, 84, 77, 82, 91, 85, 90)
Mean = 81

<h3>Standard Deviation</h3>

difference between each number and mean,

$x_1 -\mu= 76-81 = -5\\
x_2-\mu = 87-81 = 6\\
x_3-\mu = 65-81 = -16\\
x_4-\mu = 88 -81 = 7\\
x_5-\mu = 67-81 = -14\\
x_6 -\mu= 84-81 = 3\\
x_7 -\mu= 77-81 = -4\\
x_8 -\mu= 81-81 = 1\\
x_9 -\mu= 91-81 = 10\\
x_{10}-\mu=85-81 = 4\\
x_{11} -\mu= 90-81 = 9$

$\sum(x-\mu)^2 = x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2+x_9^2+x_{10}^2+x_{11}^2$

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

= 785

$\rm{ Standard\ Deviation = \sqrt{\dfrac{\sum{(X-\mu)^2}} {n}$

$\sigma= \sqrt{\dfrac{785}{11}}\\\\
\sigma = 8.4477$

<h3>Variance</h3>

Variance = $\sigma ^2$

= 71.40

Hence, the standard deviation is 8.4477 and the variance is 71.40.

Learn more about Standard Deviation:

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3 years ago

What is the percent of change from 14 inches 26 inches

PolarNik [594]

To find the percent of anything, you divide what you have from the total (or the smaller number over the bigger number). In this case, you will do 14/26.
14/26=0.53846
I'm going to round to the hundredths: 0.54
Move the decimal place two times to the right: 54
The percent change from 14 inches to 26 inches is 54%

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3 years ago

Solve the equation: -8x=32

Alexandra [31]

Answer:

−

Step-by-step explanation:

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