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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 2.2.11
Chapter 2, Problem 2.2.11

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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1
Step 1: Review the frequency distribution provided in Exercise 15 of Section 2-1. Ensure you understand the intervals (or bins) and their corresponding frequencies, as these will form the basis of the histogram.
Step 2: Set up the axes for the histogram. The horizontal axis (x-axis) will represent the intervals (or bins), and the vertical axis (y-axis) will represent the frequencies. Label both axes appropriately.
Step 3: For each interval, draw a bar whose height corresponds to the frequency of that interval. Ensure the bars are adjacent to each other without gaps, as histograms represent continuous data.
Step 4: Analyze the shape of the histogram. Look for characteristics of a normal distribution, such as a symmetric bell-shaped curve, where most data points cluster around the mean and frequencies taper off at the extremes.
Step 5: Based on the shape of the histogram, determine whether the data appears to follow a normal distribution. If the graph is symmetric and bell-shaped, it may suggest normality. If it is skewed or has multiple peaks, it may not represent a normal distribution.

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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. It consists of bars that represent the frequency of data points within specified intervals, or bins. The height of each bar indicates the number of observations that fall within that range, allowing for a visual assessment of the data's distribution shape.
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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. In a normal distribution, most of the observations cluster around the central peak, and the probabilities for values further away from the mean taper off equally in both directions. Understanding this concept is crucial for determining if a dataset approximates this idealized distribution.
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Frequency Distribution

A frequency distribution is a summary of how often each value occurs in a dataset. It can be presented in a table or graphically, such as in a histogram. This concept is essential for analyzing data, as it provides insights into the data's central tendency, variability, and overall distribution, which are foundational for statistical analysis.
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Related Practice
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 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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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 5–8, answer the questions by referring to the following Minitab-generated histogram, which depicts the weights (grams) of all quarters listed in Data Set 40 “Coin Weights” in Appendix B. (Grams are actually units of mass and the values shown on the horizontal scale are rounded.)


Sample Size What is the approximate number of quarters depicted in the three bars farthest to the left?

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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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