Question

Please help: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.Enter your answer in the box. ___

Answer 1

Given

Number of values = 9

sum of squared deviations = 316

The sum of squared deviations is related to the standard deviation s by the formula

`\begin{gathered} s\text{ = }\sqrt{(SS)/(n-1)} \\ Where\text{ SS is the sum of squared deviations} \\ and\text{ n is the number of sample} \end{gathered}`

Applying the formula to the problem:

`\begin{gathered} s\text{ = }\sqrt{(316)/(9-1)} \\ =\text{ }√(39.5) \\ =\text{ 6.2849025} \\ \approx\text{ 6.3 \lparen nearest tenth\rparen} \end{gathered}`

Answer:

standard deviation = 6.3