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

Speed Dating In a study of speed dating conducted at Columbia University, female subjects were asked to rate the attractiveness of their male dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Can the results be used to describe the attractiveness of the population of adult males?

5 8 3 8 6 10 3 7 9 8 5 5 6 8 8 7 3 5 5 6 8 7 8 8 8 7

Short answer

(a). The mean is 6.6.

(b). The median is 7.0.

(c). The mode is 8.

(d). The midrange is 6.5.

No, the results are not described for all adult males as the sample includes females from only one university.

Step-by-step solution

Given information

Female respondents at Columbia University were recorded for the attractiveness of male dates on a scale of 1 to 10.

5, 8, 3, 8, 6, 10, 3, 7, 9, 8, 5, 5, 6, 8, 8, 7, 3, 5, 5, 6, 8, 7, 8, 8, 8, 7

Compute mean

(a)

The mean is calculated for n observations as:

$\overline{x}=\frac{\sum x}{n}$, where xis the observations and nis the count of the observations.

Substitute the values in the formula.

$$\begin{gathered} \overline{x}=\frac{5+8+3+...+7}{26} \\ =\frac{171}{26} \\ \approx 6.5769 \end{gathered}$$

Thus, the mean value is approximately 6.6.

Compute median

(b)

The median is computed in the following steps.

• Sort the values.
• If n is even, the median is the average of the two middle values.
• If n is odd, the median is the middle value.

The number of observations is 26.

Arrange the observations in ascending order.

3
3
3
5
5
5
5
5
6
6
6
7
7
7
7
8
8
8
8
8
8
8
8
8
9
10

The middlemost observations are 7 and 7.

The median is given as:

$$\begin{gathered} M=\frac{7+7}{2} \\ =7 \end{gathered}$$

Thus, the median is 7.0.

Compute mode

(c)

Mode is(are) the observation(s) with the maximum frequency value.

Observations	Frequency
3	3
5	5
6	3
7	4
8	9
9	1
10	1

Thus, the mode in the data is 8.

Compute midrange

(d)

The average of the two extreme values is computed as:

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

Substitute the values in the formula.

$$\begin{gathered} \text{Midrange}=\frac{3+10}{2} \\ =\frac{13}{2} \\ =6.5 \end{gathered}$$

Thus, the midrange is 6.5.

Explain that the results are valid for the population of all adults

The population for the study is all male adults.

The sample is taken from females of Columbia University for male dates.

The sample is restricted to responses from the females of one university, and thus, it cannot represent male adults.

As the sample is not an accurate representation of the population, the results are not described for the attractiveness of all adult males.