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:

brainly.com/question/12402189

3 0

3 years ago

If the supplement of an angle is two-third of itself ,then its supplement is

stich3 [128]

( 'x' is not 144 .)

The supplement of an angle is (180 - x) .
The problem says that (2/3) of 'x' is equal to (180 - x) .

180 - x = 2/3 x

Multiply each side by 3 :
( Note: 3 x 180 = 540 .)

540 - 3x = 2x

Add 3x to each side:

540 = 5x

Divide each side by 5 :

<u>x = 108°</u> .

5 0

3 years ago

PLEASE HELP! FIRST RATIONAL ANSWER GETS BRAINLIEST! PLEASE EXPLAIN

Soloha48 [4]

Answer:

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers