Question

Rylan is calculating the standard deviation of a data set that has 9 values. He determines that the sum of the squared deviations is 316. What is the standard deviation of the data set? Round the answer to the nearest tenth

Answer 1

The formula for the sum of the squares of the deviations is
SS = s² (N -1)

We are given
SS = 316
N = 9

Substituting
316 = s² (9 - 1)
Solving for s
s = 6.28

The standard deviation is 6.28

Answer 2

Answer:

6.3

Step-by-step explanation:

We have been given that Rylan is calculating the standard deviation of a data set that has 9 values. He determines that the sum of the squared deviations is 316.      

We will use the formula $\text{Standard deviation}=\sqrt{\frac{\text{Sum of squares}}{n-1}}$, where n represents the number of data points in a data set.

Upon substituting our given values in above formula we will get,

$\text{Standard deviation}=\sqrt{\frac{316}{9-1}}$

$\text{Standard deviation}=\sqrt{\frac{316}{8}}$

$\text{Standard deviation}=\sqrt{39.5}$

$\text{Standard deviation}=6.284902544988\approx 6.3$

Therefore, the standard deviation of our given data set is 6.3.