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Ch. 2 - Exploring Data with Tables and Graphs
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 2 - Exploring Data with Tables and GraphsProblem 2.2.9
Chapter 2, Problem 2.2.9

In Exercises 9–18, construct the histograms and answer the given questions.
Chicago Commute Time Use the frequency distribution from Exercise 13 in Section 2-1 to construct a histogram. Does it appear to be the graph of data from a population with a normal distribution?

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Step 1: Review the frequency distribution provided in Exercise 13 of Section 2-1. Identify the class intervals (bins) and their corresponding frequencies. These will form the basis for constructing the histogram.
Step 2: On graph paper or using statistical software, label the x-axis with the class intervals (e.g., commute time ranges) and the y-axis with the frequencies. Ensure the axes are properly scaled to accommodate the data.
Step 3: For each class interval, draw a bar whose height corresponds to the frequency of that interval. Ensure the bars are adjacent to each other with no gaps, as histograms represent continuous data.
Step 4: Analyze the shape of the histogram. Look for characteristics such as symmetry, skewness, or the presence of a bell-shaped curve, which are indicative of a normal distribution.
Step 5: Conclude whether the histogram suggests that the data comes from a population with a normal distribution. A normal distribution typically has a symmetric, bell-shaped curve with most data concentrated around the mean and tapering off at the extremes.

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Key Concepts

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

Histogram

A histogram is a graphical representation of the distribution of numerical data, where the data is divided into intervals (bins) and the frequency of data points within each interval is represented by the height of bars. It helps visualize the shape, central tendency, and variability of the data, making it easier to identify patterns such as skewness or modality.
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Normal Distribution

Normal distribution, often referred to as a bell curve, is a probability distribution that is symmetric about the mean, indicating that data near the mean are more frequent in occurrence than data far from the mean. In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, which is crucial for understanding the spread and likelihood of data points.
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Frequency Distribution

A frequency distribution is a summary of how often each value occurs in a dataset. It organizes data into categories or intervals, allowing for easy analysis of the data's distribution. This foundational concept is essential for constructing histograms, as it provides the necessary counts for each bin that will be visually represented in the histogram.
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Related Practice
Textbook Question

Freshman 15 Refer to Data Set 13 “Freshman 15” and use the second column, which lists weights (kg) in September of college freshmen. Begin with a lower class limit of 40 kg and use a class width of 10 kg. Does the distribution appear to be a normal distribution?

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Textbook Question

Analysis of Last Digits Weights of respondents were recorded as part of the California Health Interview Survey. The last digits of weights from 50 randomly selected respondents are listed below. Construct a frequency distribution with 10 classes. Based on the distribution, do the weights appear to be reported or actually measured? Does there appear to be a gap in the frequencies and, if so, how might that gap be explained? What do you know about the accuracy of the results?

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Textbook Question

Births Natural births randomly selected from four hospitals in New York State occurred on the days of the week (in the order of Monday through Sunday) with these frequencies: 52, 66, 72, 57, 57, 43, 53. Does it appear that such births occur on the days of the week with equal frequency?

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Textbook Question

In Exercises 5–8, identify the class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. The frequency distributions are based on real data from Appendix B.

8.

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Textbook Question

In Exercises 15 and 16, construct the frequency polygons.


Chicago Commute Times Use the frequency distribution from Exercise 13 in Section 2-1 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?


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Textbook Question

In Exercises 9–18, construct the histograms and answer the given questions.


Old Faithful Use the frequency distribution from Exercise 15 in Section 2-1 to construct a histogram. Does it appear to be the graph of data from a population with a normal distribution?

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