Graphing Data Sets In Exercises 17–32, organize the data using the indicated type of graph. Describe any patterns.


Highest-Paid Athletes Use a stem-and-leaf plot that has two rows for each stem to display the data, which represent the incomes (in millions) of the top 30 highest-paid athletes. (Source: Forbes Media LLC)
39 42 41 45 48 48 106 45 88 54 61 37 62 74 40
47 56 57 105 96 37 48 41 64 52 47 45 59 49 104

Verified step by step guidance

1. Step 1: Understand the stem-and-leaf plot. A stem-and-leaf plot is a way to organize numerical data by splitting each value into a 'stem' (all but the last digit) and a 'leaf' (the last digit). For this problem, we will use two rows for each stem to better display the data.
2. Step 2: Sort the data in ascending order. This will make it easier to organize the values into the stem-and-leaf plot. The sorted data is: 37, 37, 39, 41, 41, 42, 45, 45, 45, 47, 47, 48, 48, 48, 49, 52, 54, 56, 57, 59, 61, 62, 64, 74, 88, 96, 104, 105, 106.
3. Step 3: Define the stems and leaves. The 'stem' will represent the tens place of each number, and the 'leaf' will represent the ones place. For example, the number 37 will have a stem of 3 and a leaf of 7. Since we are using two rows per stem, the first row will include leaves from 0–4, and the second row will include leaves from 5–9.
4. Step 4: Organize the data into the stem-and-leaf plot. For each stem, place the corresponding leaves in the appropriate row. For example, for the stem '3', the first row will include the leaf '7' (from 37), and the second row will include another '7' (from the second 37) and '9' (from 39). Repeat this process for all stems.
5. Step 5: Analyze the plot for patterns. Once the stem-and-leaf plot is complete, look for any trends or clusters in the data. For example, you might notice that most of the incomes are concentrated in the 40s and 50s, with a few outliers in the 100s. This can help describe the distribution of the data.

Key Concepts

Stem-and-Leaf Plot

A stem-and-leaf plot is a method of displaying quantitative data in a graphical format, similar to a histogram, to retain the original data values while showing their distribution. Each number is split into a 'stem' (the leading digit or digits) and a 'leaf' (the trailing digit). This type of plot allows for easy visualization of the data's shape and helps identify patterns, such as clusters or gaps.

Data Organization

Data organization refers to the systematic arrangement of data to facilitate analysis and interpretation. In statistics, organizing data into graphs or tables helps to summarize information, making it easier to identify trends, patterns, and outliers. Proper organization is crucial for effective data visualization, which aids in drawing meaningful conclusions from the data set.

Describing Patterns

Describing patterns in data involves analyzing the visual representation to identify trends, clusters, or anomalies. This can include noting the distribution of values, such as whether they are concentrated in a particular range or if there are any noticeable gaps. Recognizing these patterns is essential for making informed interpretations and decisions based on the data presented.