Question

question 4 (1 point)
the shoe size for all the pairs of shoes in a persons closet are recorded.
7 7 7 7 7 7 7 7
7 7

1. what is the mean? ________
2. what is the standard deviation? ________

blank 1:
blank 2:

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}$ of a data - set $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, the data - set is $x_1 = x_2=\cdots=x_9 = 7$, and $n = 9$. So, $\sum_{i = 1}^{9}x_i=7 + 7+\cdots+7=7\times9 = 63$, and $\bar{x}=\frac{63}{9}=7$.

Step2: Calculate the standard deviation

The formula for the standard deviation $s$ of a sample is $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}$. Since $x_i = 7$ for all $i$ from $1$ to $9$ and $\bar{x}=7$, then $(x_i-\bar{x})=(7 - 7)=0$ for all $i$. So, $\sum_{i = 1}^{9}(x_i - 7)^2=0$. Then $s=\sqrt{\frac{0}{9 - 1}}=0$.

Answer:

Blank 1: 7
Blank 2: 0