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? 234 160 119 131 218 207 146 141 The range of the sample data is? The Standard deviation of the sample data is? The variance of the sample data is? How useful are the measures of variation for someone searching for a​ room? A. The measures of variation are not very useful because when searching for a​ room, low​ prices, location, and good accommodations are more important than the amount of variation in the area. B. The measures of variation are very useful because a person does not want to buy a room where the variation is too low. C. The measures of variation are not very useful because the values are nominal data that do not measure or count​ anything, so the resulting statistics are meaningless. D. The measures of variation are very useful because a person does not want to buy a room where the variation is too high.

Answer 1

Range = 115$

Standard Deviation = 43.76$

Variance = 1915.142$

Option A) The measures of variation are not very useful because when searching for a​ room, low​ prices, location, and good accommodations are more important than the amount of variation in the area.

Explanation:

We are given the data for prices in dollars for one night at different hotels in a certain region.

234, 160, 119, 131, 218, 207, 146, 141

Range:

Sorted data: 119, 131, 141, 146, 160, 207, 218, 234

`\text{Range} = 234-119 = 115\$`

Standard Deviation:

`\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}`

where
`x_i` are data points,
`\bar{x}` is the mean and n is the number of observations.

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

`Mean =\displaystyle(1356)/(8) = 169.5`

Sum of squares of differences = 4160.25 + 90.25 + 2550.25 + 1482.25 + 2352.25 + 1406.25 + 552.25 + 812.25 = 13406

`\sigma = \sqrt{(13406)/(7)} = 43.76\$`

Variance =

`\sigma^2 = 1915.142\$`

Measure of variance for someone searching for room:

Option A) The measures of variation are not very useful because when searching for a​ room, low​ prices, location, and good accommodations are more important than the amount of variation in the area.