Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

2. Describing Data with Tables and Graphs

Histograms

Statistics

2. Describing Data with Tables and Graphs

Histograms

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1:18 minutes

Problem 2.1.19a

Textbook Question

Use the frequency histogram
a. to determine the number of classes.

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Step 1: Observe the histogram provided. A histogram is a graphical representation of the distribution of data using bars, where each bar represents a class interval and its height corresponds to the frequency of data within that interval.

Step 2: Identify the class intervals on the x-axis. In this histogram, the intervals are labeled as 34.5-44.5, 44.5-54.5, 54.5-64.5, 64.5-74.5, 74.5-84.5, and 84.5-94.5.

Step 3: Count the number of distinct class intervals. Each interval represents a class, and the total number of intervals gives the number of classes.

Step 4: Verify that the intervals are non-overlapping and cover the entire range of the data. This ensures that the histogram is properly constructed and the number of classes is accurate.

Step 5: Conclude the number of classes based on the count from Step 3. In this case, there are six distinct class intervals visible in the histogram.

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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 the distribution of numerical data. It displays the frequency of data points within specified intervals, known as bins or classes. Each bar's height corresponds to the number of observations in that interval, allowing for a visual interpretation of the data's distribution and central tendencies.

Classes (Bins)

In the context of a histogram, classes (or bins) are the intervals into which the data is divided. The choice of the number of classes can affect the histogram's appearance and the insights drawn from it. A well-chosen number of classes helps to reveal patterns in the data, such as peaks and gaps, while too few or too many can obscure important information.

Determining the Number of Classes

Determining the number of classes for a histogram is crucial for effective data visualization. Common methods include Sturges' rule, which suggests using the formula k = 1 + 3.322 log(n), where k is the number of classes and n is the number of data points. This approach helps balance detail and clarity, ensuring that the histogram accurately represents the data's distribution.

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Related Practice

Textbook Question

Win 4 Lottery Shown below is a histogram of digits selected in California’s Win 4 lottery. Each drawing involves the random selection (with replacement) of four digits between 0 and 9 inclusive.

c. Identify the frequencies, then test the claim that the digits are selected from a population in which the digits are all equally likely. Is there a problem with the lottery?

Textbook Question

Graphical Analysis In Exercises 9–12, determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer.

Textbook Question

Song Lengths Side-by-side box-and-whisker plots can be used to compare two or more different data sets. Each box-and-whisker plot is drawn on the same number line to compare the data sets more easily. The lengths (in seconds) of songs played at two different concerts are shown.

d. Can you determine which concert lasted longer? Explain.

Textbook Question

Use the frequency histogram

d. describe any patterns with the data..

Textbook Question

Use the frequency histogram

describe any patterns with the data..

Textbook Question

Use the relative frequency histogram to

approximate the greatest and least relative frequencies.

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

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Use the frequency histograma. to determine the number of classes.

Key Concepts

Frequency Histogram

Classes (Bins)

Determining the Number of Classes

Watch next

Use the frequency histogram
a. to determine the number of classes.