Question

What is the standard deviation of this data set?

Answer 1

Answer:

D. 24.7

Step-by-step explanation:

First off we need to find the Mean of the data set. We take sum of all the data in the set and divide it by the number of sample in the data set.

$Mean=\dfrac{12+16+22+23+23+34+44+46+47+48+64+67+73+83+89}{15}$

$Mean=\dfrac{691}{15}$

$Mean=46.07$

Now we find the variance using the formula:

σ²=Σ(x-Mean)²

       n-1

σ²=$\dfrac{(12-46.07)^{2}+(16-46.07)^{2}+(22-46.07)^{2}+...+(89-46.07)^{2}}{15-1}$

σ²=$\dfrac{8,554.934}{14}$

σ²=611.07

Now that we have the variance, we can use the variance to solve for the standard deviation by getting the square root of the variance.

SD=$\sqrt{611.07}$

SD=24.72