Question

jordyn asked 8 people how many apps they each had on their phone. here are their responses: 21,28,31,46,55,60,65,70 the mean is $\bar{x}=47$ apps. which of these formulas gives the standard deviation? choose 1 answer: (a) $s_x = sqrt{\frac{(21 - 8)^2+(28 - 8)^2+cdots+(70 - 8)^2}{47}}$ (b) $s_x = sqrt{\frac{(21 - 47)^2+(28 - 47)^2+cdots+(70 - 47)^2}{7}}$

Explanation:

Step1: Recall standard - deviation formula

The formula for the sample standard deviation $s_x$ of a data - set $x_1,x_2,\cdots,x_n$ with mean $\bar{x}$ is $s_x=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}$. Here, $n = 8$ (the number of data points) and $\bar{x}=47$.

Step2: Analyze each option

In option A, $8$ is subtracted from each data - point instead of the mean $\bar{x}=47$, and the denominator is the mean instead of $n - 1$. In option B, we subtract the mean $\bar{x}=47$ from each data - point, and since $n = 8$, $n-1=7$, which is in the denominator. This is consistent with the sample standard - deviation formula.

Answer:

B. $s_x=\sqrt{\frac{(21 - 47)^2+(28 - 47)^2+\cdots+(70 - 47)^2}{7}}$