Answer to Question #143876 in Statistics and Probability for Vladimyr Lubin

Question

Listed below are prices in dollars for one night at different hotels in a certain region. Find the​ range, variance, and standard deviation for the given sample data. Include appropriate units in the results. How useful are the measures of variation for someone searching for a​ room?
91,77,250,241,120,258,137,135

Answer 1

We assume that all prices are in dollars. The range is the difference between the lowest and the highest value:

$r=258-77=181\$$,

The mean is:

$\bar{x}=\frac{91+77+250+241+120+258+137+135}{8}=163.625\$,$

The variance is:

$\sigma^2=\frac{(91-\bar{x})^2+(77-\bar{x})^2+(250-\bar{x})^2+(241-\bar{x})^2+(120-\bar{x})^2+(258-\bar{x})^2+(137-\bar{x})^2+(135-\bar{x})^2}{8}\approx4820.4844\$^2$

The standard deviation is a square root of the variance:

$\sigma=69.4297\$$

Variation shows that the prices are quite different. The ratio of variance and the number of values shows the difference of prices.