listed below are prices in dollars for one night at different hotels in a certain region. find the range…

Explanation:

Step1: Calculate the mean

First, find the sum of the data values: $250 + 289+190 + 122+219+194+75+108=1447$. There are $n = 8$ data - points. The mean $\bar{x}=\frac{1447}{8}=180.875$ dollars.

Step2: Calculate the squared differences

For each data - point $x_i$, calculate $(x_i-\bar{x})^2$. For $x_1 = 250$: $(250 - 180.875)^2=(69.125)^2 = 4778.265625$. For $x_2 = 289$: $(289 - 180.875)^2=(108.125)^2 = 11690.515625$. For $x_3 = 190$: $(190 - 180.875)^2=(9.125)^2 = 83.265625$. For $x_4 = 122$: $(122 - 180.875)^2=(-58.875)^2 = 3467.265625$. For $x_5 = 219$: $(219 - 180.875)^2=(38.125)^2 = 1453.515625$. For $x_6 = 194$: $(194 - 180.875)^2=(13.125)^2 = 172.265625$. For $x_7 = 75$: $(75 - 180.875)^2=(-105.875)^2 = 11218.515625$. For $x_8 = 108$: $(108 - 180.875)^2=(-72.875)^2 = 5317.765625$.

Step3: Calculate the variance

The sample variance $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}$. $\sum_{i = 1}^{8}(x_i-\bar{x})^2=4778.265625+11690.515625+83.265625+3467.265625+1453.515625+172.265625+11218.515625+5317.765625 = 38181.375$. $s^2=\frac{38181.375}{7}\approx5454.5$.

Step4: Calculate the standard deviation

The sample standard deviation $s=\sqrt{s^2}=\sqrt{5454.5}\approx73.8$ dollars.

Answer:

The standard deviation of the sample data is $73.8$ dollars.