Question

the table to the right gives the average sales tax rate (state plus local) in six east - coast states and six western states. complete parts (a) through (e) below.
c. find the standard deviation for each of the data sets.
the standard deviation for the east coast states is
(type an integer or decimal rounded to three decimal places as needed.)
choose the correct boxplot for the west coast states below.
(type integers or decimals rounded to three decimal places as needed.)
0.000
1.620
7.220
7.500
8.910
east coast states
6.80%
5.75%
5.00%
0.00%
8.99%
8.00%
west coast states
7.50%
1.62%
0.00%
8.91%
7.50%
6.94%

Explanation:

Step1: Recall standard - deviation formula

The formula for the standard deviation of a sample is $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$, where $x_{i}$ are the data - points, $\bar{x}$ is the sample mean, and $n$ is the sample size.

Step2: Calculate the mean

For the east - coast states data set (let's assume the data values are $x_1,x_2,\cdots,x_n$), first find the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$.

Step3: Calculate the squared differences

Calculate $(x_{i}-\bar{x})^{2}$ for each $i$ from $1$ to $n$.

Step4: Sum the squared differences

Find $\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}$.

Step5: Calculate the standard deviation

Divide the sum of squared differences by $n - 1$ and then take the square - root: $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$.
Since the data values for the east - coast states are not given in the text (only the task description is visible), we cannot perform the actual calculations. But if we assume the data set for east - coast states is $x_1 = 6.80,x_2=5.75,x_3 = 5.00,x_4=0.00,x_5 = 8.99,x_6=8.00$:

1. Calculate the mean $\bar{x}=\frac{6.80 + 5.75+5.00 + 0.00+8.99+8.00}{6}=\frac{34.54}{6}\approx5.757$.
2. Calculate $(x_{1}-\bar{x})^{2}=(6.80 - 5.757)^{2}\approx1.109$, $(x_{2}-\bar{x})^{2}=(5.75 - 5.757)^{2}\approx0.000049$, $(x_{3}-\bar{x})^{2}=(5.00 - 5.757)^{2}\approx0.573$, $(x_{4}-\bar{x})^{2}=(0.00 - 5.757)^{2}\approx33.143$, $(x_{5}-\bar{x})^{2}=(8.99 - 5.757)^{2}\approx10.454$, $(x_{6}-\bar{x})^{2}=(8.00 - 5.757)^{2}\approx5.032$.
3. $\sum_{i = 1}^{6}(x_{i}-\bar{x})^{2}\approx1.109+0.000049 + 0.573+33.143+10.454+5.032\approx50.311$.
4. $s=\sqrt{\frac{50.311}{6 - 1}}=\sqrt{10.0622}\approx3.172$.

However, without the actual data from the full problem, we cannot give a definite answer. If we assume the data is correctly inputted into a statistical software or calculator, and the correct calculation is done:

Answer:

(No definite answer as data is not fully provided in the image. If we assume sample data as above, the answer is approximately $3.172$)