Textbook Question
Use the frequency histogram
a. to determine the number of classes.
Ch. 2 - Descriptive Statistics
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 2, Problem 2.T.2b
The data set represents the number of movies that a sample of 20 people watched in a year.
121 148 94 142 170 88 221 106 18 67
149 28 60 101 134 168 92 154 53 66
b. Display the data using a frequency histogram and a frequency polygon on the same axes.
Verified step by step guidance1
Step 1: Organize the data by determining the range. Find the minimum and maximum values in the data set to understand the spread. The minimum is the smallest number, and the maximum is the largest number in the data.
Step 2: Decide on the number of class intervals (bins) for the histogram. A common rule of thumb is to use between 5 and 10 bins for a data set of this size. Calculate the class width using the formula: \(\text{Class Width} = \frac{\text{Maximum} - \text{Minimum}}{\text{Number of Classes}}\), then round up to a convenient number.
Step 3: Create the frequency distribution table by listing the class intervals and counting how many data points fall into each interval. This frequency count will be used to plot the histogram and frequency polygon.
Step 4: Draw the frequency histogram by plotting the class intervals on the horizontal axis and the frequencies on the vertical axis. For each class interval, draw a bar whose height corresponds to the frequency of that interval. Ensure the bars are adjacent with no gaps to represent continuous data.
Step 5: To draw the frequency polygon on the same axes, first find the midpoints of each class interval using \(\text{Midpoint} = \frac{\text{Lower Class Limit} + \text{Upper Class Limit}}{2}\). Then plot points at these midpoints with heights equal to the corresponding frequencies. Connect these points with straight lines. Optionally, add points at the beginning and end with zero frequency to close the polygon.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Frequency Histogram
A frequency histogram is a graphical representation of data where the data range is divided into intervals called bins, and the height of each bar shows the number of data points within each bin. It helps visualize the distribution and frequency of data values, making patterns and skewness easier to identify.
Recommended video:
Guided course
05:54
Intro to Histograms
Frequency Polygon
A frequency polygon is a line graph that connects the midpoints of the tops of the bars in a histogram. It provides a clear view of the shape of the data distribution and is useful for comparing multiple data sets on the same axes by showing trends and frequencies smoothly.
Recommended video:
04:41Creating Frequency Polygons
Data Grouping and Class Intervals
Data grouping involves organizing raw data into class intervals or bins to simplify analysis and visualization. Choosing appropriate class widths and intervals is essential for accurately representing the data distribution in histograms and frequency polygons without losing important details.
Recommended video:
4:01Introduction to Collecting Data
Related Practice
Textbook Question
Use the frequency distribution in Exercise 4 to estimate the sample mean and sample standard deviation of the data. Do the formulas for grouped data give results that are as accurate as the individual entry formulas? Explain.
Textbook Question
The mean gestational length of a sample of 208 horses is 343.7 days, with a standard deviation of 10.4 days. The data set has a bell-shaped distribution.
b. Determine whether a gestational length of 318.4 days is unusual.
Textbook Question
The table lists the number of albums by The Beatles that received sales certifications. Display the data using (b) a Pareto chart. (Source: Recording Industry Association of America)
Textbook Question
Extending Concepts
Golf The distances (in yards) for nine holes of a golf course are listed.
336 393 408 522 147 504 177 375 360
a. Find the mean and the median of the data.
Textbook Question
The number of minutes it took 12 students in a statistics class to complete the final exam are listed. Use a scatter plot to display this data set and the data set in Exercise 1. The data sets are in the same order. Describe any patterns.
61 85 67 48 54 61 59 80 67 55 88 84