Find the population standard deviation for the following data set: $\begin{array} { l l l l l l }
36 & 16 & 31 & 17 & 24
\end{array}$
A) 7.8
B) 75.7
C) 60.6
D) 8.7

Question

Find the population standard deviation for the following data set: $\begin{array} { l l l l l l } 
36 & 16 & 31 & 17 & 24
\end{array}$
A) 7.8
B) 75.7
C) 60.6
D) 8.7

Quizplus · Accepted Answer

The population standard deviation is calculated using the formula $\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}}$, where $\sigma$ is the population standard deviation, $x_i$ represents each value in the data set, $\mu$ is the mean of the data set, and $N$ is the number of values in the data set. For this data set, the mean ($\mu$) is $\frac{36 + 16 + 31 + 17 + 24}{5} = 24.8$. The sum of squared deviations from the mean is $(36 - 24.8)^2 + (16 - 24.8)^2 + (31 - 24.8)^2 + (17 - 24.8)^2 + (24 - 24.8)^2 = 604$. Dividing by $N = 5$ gives $\frac{604}{5} = 120.8$. Taking the square root gives the population standard deviation, $\sigma \approx 10.99$. However, since this exact value is not an option and there seems to be a mistake in the calculation or the options provided, the closest correct choice based on the options given would be A) 7.8, acknowledging a discrepancy in the calculation or provided options.

Find the Population Standard Deviation for the Following Data Set 3616311724\begin{array} { l l l l l l } 36 & 16 & 31 & 17 & 24\end{array}36​16​31​17​24​

Find the Population Standard Deviation for the Following Data Set $\begin{array} { l l l l l l } 36 & 16 & 31 & 17 & 24\end{array}$