Question

Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question.

Listed below are prices in dollars for one night at different hotels located on Las Vegas Boulevard (the “Strip”).

If you decide to stay at one of these hotels, what statistic is most relevant, other than the measures of center?

Apart from price, identify one other important factor that would affect your choice.

212 77 121 104 153 264 195 244

Short answer

(a) The mean is $171.3.

(b) The median is $174.0.

(c) Mode: None

(d) The midrange is $170.5.

The lowest price of the hotel is another most relevant measure.

The factors which affect the choice are services, location, etc.

Step-by-step solution

Given information

The prices(in dollars) for one night stay at eight different hotels in Las Vegas are:

212, 77, 121, 104, 153, 264, 195, 244

Compute mean

(a)

The expression used to calculate the sample mean is:

$\overline{x}=\frac{\sum x}{n}$, wherexrepresents the values and n is the sample size.

Substitute the values in the formula.

$$\begin{gathered} \overline{x}=\frac{212+77+...+244}{8} \\ =\frac{1370}{8} \\ \approx 171.3 \end{gathered}$$

Thus, the mean value is approximately $171.3.

Compute median

(b)

The following criteria are used to obtain the median once the set of observations are arranged.

Case 1: n is odd

The middlemost observation is the median.

Case 2: n is even

The average of the two middle observations is the median.

The number of observations is 8.

Arrange the observations in an ascending order.

77
104
121
153
195
212
244
264

The middlemost observations are 153 and 195.

The median is given as:

$$\begin{gathered} M=\frac{153+195}{2} \\ =174 \end{gathered}$$

Thus, the median is $174.0.

Compute mode

(c)

The mode is/are the value(s) with the maximum frequency.

The frequency distributions for the prices of hotels are:

Prices	Frequency
77	1
104	1
121	1
153	1
195	1
212	1
244	1
264	1

As no price repeats itself more than once, there is no mode for the data.

Compute midrange

(d)

The following formula is used for computing midrange:

$\text{Midrange}=\frac{\text{Minimum}\text{value}+\text{Maximum}\text{value}}{2}$

Substitute the values in the formula.

$$\begin{gathered} \text{Midrange}=\frac{77+264}{2} \\ =\frac{341}{2} \\ =170.5 \end{gathered}$$

Thus, the midrange is $170.5.

State the other statistic that is the most relevant to the study 

The relevant statistic other than the measures of the center is the minimum price of the hotel. It will help the individuals to gain the base level of price for any hotel in Las vegas boulevard.

State factors other than price which would affect the decision

The other factors that may affect the decision for choosing the hotel are:

• the location of the hotel,
• the reviews of services by other tourists, and
• the ratings of the hotel.