Find the variance and the standard deviation (correct to two decimal places) of the following data set. $5,6,6,7,8,9,16,20$
A) variance: $25.73$ standard deviation: $5.07$
B) variance: $5.07$ standard deviation: $25.73$
C) variance: $25.73$ standard deviation: $662.26$
D) variance: $92.64$ standard deviation: $25.73$
E) variance: $9.63$ standard deviation: $3.10$

Question

Quizplus · Accepted Answer

To find the variance, we first need to find the mean:
$$\bar{x}=\frac{5+6+6+7+8+9+16+20}{8}=9$$
Then we can use the formula for variance:
$$s^2=\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2$$
Plugging in the values, we get:
$$s^2=\frac{1}{7}( (-4)^2+(-3)^2+(-3)^2+(-2)^2+(-1)^2+0^2+7^2+11^2 )=25.73$$
To find the standard deviation, we just take the square root of the variance:
$$s=\sqrt{25.73}=5.07$$
Therefore, the answer is A.

Find the Variance and the Standard Deviation (Correct to Two 5,6,6,7,8,9,16,205,6,6,7,8,9,16,205,6,6,7,8,9,16,20

Find the Variance and the Standard Deviation (Correct to Two $5,6,6,7,8,9,16,20$