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The given data shows the prices for one night at eight different hotels in Las Vegas.

The number of values (n) is 8.

The measures of dispersion are used for analyzing the spread of a given set of values.

The following are the three highly used measures of variation:

The rangeis the value obtained when the minimum value is subtracted from the maximum value.

$$\begin{gathered} \text{Range}=\text{Maximum}\text{Value}-\text{Minimum}\text{Value} \\ =264-77 \\ =187.0\text{dollars} \end{gathered}$$

.

Therefore, for the given sample of prices, the range is equal to 187.0 dollars.

Sample variance$\left(s^2\right)$is used to determine the inherent variation in the sample. The square of the unit of the data forms the unit of variance. It is calculated using the following formula:

$s^2=\frac{{鈭�}_{1=1}^n{\left(x_i-\stackrel{炉}{x}\right)}^2}{n-1}$

Here,

x represents the sampled values, and

$\stackrel{炉}{x}$is the sample mean.

The sample mean is calculated as

$$\begin{gathered} \stackrel{炉}{x}=\frac{{鈭�}_{1=1}^n{x}_i}{n} \\ =\frac{212+77+...+244}{8} \\ =\frac{1370}{8} \\ 鈮�171.3 \end{gathered}$$

.

Thus, the sample mean is 171.3 million.

The variance of the sample is calculated as

$$\begin{gathered} s^2=\frac{{鈭�}_{i=1}^n{\left(x_i-\stackrel{炉}{x}\right)}^2}{n-1} \\ =\frac{{\left(212-171.3\right)}^3+{\left(77-171.3\right)}^3+...+{\left(244-171.3\right)}^3}{8-1} \\ =\frac{32383.5}{7} \\ =4626.2 \end{gathered}$$

.

Therefore, the sample variance of the prices for a one-night stay is equal to 4626.2${\left(\text{dollars}\right)}^2$.

Thestandard deviation of the sample also shows the variation in the data. The units of the values in the data are the units of standard deviation. It is calculated using the following formula as

$$\begin{gathered} s=\sqrt{s^2} \\ =\sqrt{4626.2} \\ 鈮�68.0\text{dollars} \end{gathered}$$

Therefore, the sample standard deviation of the prices for a one-night stay is equal to 68.0 dollars.

As the sample consists of a range of eight different hotels with different prices, it can be said that the values of the measures of variation are useful for a person looking for a room on Las Vegas Boulevard.