Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

2. Describing Data with Tables and Graphs

Stemplots (Stem-and-Leaf Plots)

Statistics

2. Describing Data with Tables and Graphs

Stemplots (Stem-and-Leaf Plots)

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2:26 minutes

Problem 2.T.1d

Textbook Question

The overall averages of 12 students in a statistics class prior to taking the final exam are listed.
67 72 88 73 99 85 81 87 63 94 68 87

d. Display the data in a stem-and-leaf plot. Use one line per stem.

Verified step by step guidance

Step 1: Understand the stem-and-leaf plot. A stem-and-leaf plot is a way to organize numerical data by separating each value into a 'stem' (all but the last digit) and a 'leaf' (the last digit). For example, the number 67 would have a stem of 6 and a leaf of 7.

Step 2: Identify the range of the data. The smallest value is 63, and the largest value is 99. This means the stems will range from 6 to 9 (representing the tens place).

Step 3: Create the stems. Write down the stems (6, 7, 8, and 9) in a vertical column, each on its own line. These represent the tens place of the numbers.

Step 4: Assign the leaves to their respective stems. For each number in the data set, write the last digit (the leaf) next to the corresponding stem. For example, for the number 67, write the leaf 7 next to the stem 6. Repeat this for all numbers in the data set.

Step 5: Organize the leaves in ascending order for each stem. Once all the leaves are assigned, sort them in increasing order for each stem to make the plot easier to read. For example, if the leaves for stem 6 are 7, 3, and 8, rearrange them as 3, 7, 8.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stem-and-Leaf Plot

A stem-and-leaf plot is a method of displaying quantitative data in a graphical format, similar to a histogram, that helps visualize the distribution of the data. Each number is split into a 'stem' (the leading digit or digits) and a 'leaf' (the trailing digit). This format retains the original data values while providing a clear view of the data's shape and distribution.

Data Organization

Organizing data is crucial for effective analysis and interpretation. In the context of a stem-and-leaf plot, data must be sorted in ascending order to accurately represent the distribution. This organization allows for easier identification of patterns, such as clusters or gaps in the data, which can inform further statistical analysis.

Descriptive Statistics

Descriptive statistics summarize and describe the main features of a dataset. Key measures include the mean, median, mode, and range, which provide insights into the central tendency and variability of the data. Understanding these concepts is essential for interpreting the results displayed in a stem-and-leaf plot and for making informed conclusions about the dataset.

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Related Practice

Multiple Choice

A stemplot contains the row 2|0024555789. List the data points displayed in this row.

Textbook Question

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

Nursing Use a stem-and-leaf plot to display the data, which represent the number of hours 24 nurses work per week.

40 40 35 48 38 40 36 50 32 36 40 35

30 24 40 36 40 36 40 39 33 40 32 38

Textbook Question

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

Textbook Question

Yoga Classes The data sets at the left show the ages of all participants in two yoga classes.

a. Make a back-to-back stem-and-leaf plot as described in Exercise 41 to display the data.

Textbook Question

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

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Textbook Question

Estimating Standard Deviation Both data sets shown in the stem-and-leaf plots have a mean of 165. One has a standard deviation of 16, and the other has a standard deviation of 24. By looking at the stem-and-leaf plots, which is which? Explain your reasoning.

Multiple Choice

A stemplot contains the row 2|0024555789. List the data points displayed in this row.

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