Question

The accompanying data are a subset of data read from a graph in the paper "Ladies First? A Field Study of Discrimination in Coffee Shops" (Applied Economics [April, 2008]). The data are the waiting time (in seconds) between ordering and receiving coffee for 19 male customers at a Boston coffee shop. \(\begin{array}{llllllllll}40 & 60 & 70 & 80 & 85 & 90 & 100 & 100 & 110 & 120\end{array}\) \(\begin{array}{lllllllll}125 & 125 & 140 & 140 & 160 & 160 & 170 & 180 & 200\end{array}\) Use these data to construct a boxplot. Write a few sentences describing the important characteristics of the boxplot.

Short answer

The boxplot shows a slightly right-skewed distribution of the waiting times. The median waiting time is 120 seconds, with the middle 50% of waiting times ranging from 87.5 to 150 seconds. The shortest waiting time is 40 seconds, and the longest is 200 seconds. There are no outliers.

Step-by-step solution

Arrange the Data in Ascending Order

Starting with, the given data should be sorted in ascending order: 40, 60, 70, 80, 85, 90, 100, 100, 110, 120, 125, 125, 140, 140, 160, 160, 170, 180, 200.

Identify The Five-Number Summary

The five-number summary includes the minimum value (40), the first quartile (Q1), the median (Q2, the central value), the third quartile (Q3), and the maximum value (200).

Determine the Quartiles

To find the quartiles: \n- Calculate Q1: It's the median of the lower half of the data. It should be the average of the 5th and 6th values, \(Q1 = (85 + 90) / 2 = 87.5\). \n- Calculate Q2: It's the median of all the data. As an odd number of data points, it is the 10th value, \(Q2 = 120 \). \n- Calculate Q3: It's the median of the upper half of the data. It should be the average of the 14th and 15th data points, \(Q3 = (140 + 160) / 2 = 150 \).

Construct the Boxplot

Draw a number line from the minimum to the maximum. Above it, draw a rectangle that represents the interquartile range (IQR) extending from Q1 to Q3. Draw a line inside the box to indicate Q2. Extend 'whiskers' from the box to the minimum(left whisker) and maximum(right whisker) data points.

Analyze the Boxplot

The boxplot plot provides a visual summary of the central tendency, variability, and skewness of the coffee waiting time data set. The data we have is slightly skewed to the right because the right whisker is longer than the left (i.e., the maximum Q3 distance is greater than Q1's minimum distance). There are no outliers in this dataset.