Putting Graphs in Context In Exercises 5–8, match the plot with the description of the sample.
a. Times (in minutes) it takes a sample of employees to drive to work
b. Grade point averages of a sample of students with finance majors
c. Top speeds (in miles per hour) of a sample of high-performance sports cars
d. Ages (in years) of a sample of residents of a retirement home

Verified step by step guidance

1. Step 1: Analyze the stem-and-leaf plot provided. The key indicates that '0|8' represents 0.8. This means the data values are in decimal format, and each stem represents the integer part while the leaf represents the decimal part.
2. Step 2: List the data values from the stem-and-leaf plot. For example, the first row (stem 0, leaf 8) corresponds to 0.8, the second row (stem 1, leaves 5, 6, 8) corresponds to 1.5, 1.6, and 1.8, and so on.
3. Step 3: Consider the context of the data. The values range from 0.8 to 4.0, which suggests that the data could represent measurements that are typically small in magnitude, such as grade point averages (GPAs).
4. Step 4: Match the data to the given descriptions. The data does not seem to represent times to drive to work (which are usually larger numbers), top speeds of sports cars (which are much larger), or ages of retirement home residents (which are integers and larger). The data aligns best with GPAs of finance majors.
5. Step 5: Conclude that the stem-and-leaf plot matches description (b): 'Grade point averages of a sample of students with finance majors.'

Key Concepts

Data Representation

Data representation refers to the way in which data is organized and displayed for analysis. In the context of the question, the image shows a frequency distribution or a stem-and-leaf plot, which helps visualize the distribution of a dataset. This method allows for easy identification of the shape of the data, central tendencies, and potential outliers.

Descriptive Statistics

Descriptive statistics summarize and describe the main features of a dataset. Key measures include mean, median, mode, and standard deviation. Understanding these statistics is essential for interpreting the data represented in the graphs and plots, as they provide insights into the overall trends and characteristics of the sample being analyzed.

Contextual Analysis

Contextual analysis involves interpreting data within the framework of its real-world application. In this question, matching plots with descriptions requires understanding the context of each sample, such as employee commute times or student GPAs. This analysis helps in making informed conclusions about the data and its implications in practical scenarios.