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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1:58 minutes

Problem 2.3.9

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.

Verified step by step guidance

Observe the histogram provided. Note the distribution of frequencies across the bins, which represent ranges of values (e.g., 25,000 to 85,000).

Identify the general trend of the bars. In this histogram, the bars are tallest on the left side and gradually decrease in height as you move to the right.

Understand the concept of skewness. A distribution is skewed right if the tail extends to the right (towards higher values) and skewed left if the tail extends to the left (towards lower values). Symmetric distributions have equal tails on both sides, and uniform distributions have bars of roughly equal height.

Compare the histogram's shape to these definitions. The histogram shows a long tail extending to the right, indicating that the distribution is skewed right.

Justify the conclusion: The majority of the data is concentrated on the lower end (left side), with fewer occurrences as the values increase, which is characteristic of a right-skewed 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, 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 of the data distribution, making it easier to identify patterns such as symmetry, skewness, and modality.

Distribution Shape

The shape of a distribution refers to the way data points are spread across the range of values. Common shapes include symmetric (equal on both sides), uniform (equal frequency across intervals), skewed left (tail on the left), and skewed right (tail on the right). Understanding the shape is crucial for interpreting data characteristics and making statistical inferences.

Skewness

Skewness measures the asymmetry of a distribution. A distribution is skewed left if it has a longer tail on the left side, indicating that most data points are concentrated on the right. Conversely, a skewed right distribution has a longer tail on the right side. Identifying skewness helps in understanding the underlying data trends and potential outliers.

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Related Practice

Textbook Question

In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B

Histogram Construct the histogram corresponding to the frequency distribution from Exercise 1. For the values on the horizontal axis, use the class midpoint values. Which of the following comes closest to describing the distribution: uniform, normal, skewed left, skewed right?

Textbook Question

In Exercises 5 and 6, construct the dotplot.

Pulse Rates Listed below are pulse rates (beats per minute) of females selected from Data Set 1 “Body Data” in Appendix B. All of those pulse rates are even numbers. Is there a pulse rate that appears to be an outlier? What is its value?

Textbook Question

In Exercises 5 and 6, construct the dotplot.

Diastolic Blood Pressure Listed below are diastolic blood pressure measurements (mm Hg) of females selected from Data Set 1 “Body Data” in Appendix B. All of the values are even numbers. Are there any outliers? If so, identify their values.

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

a. to determine the number of classes.

Textbook Question

Use the frequency histogram

d. describe any patterns with the data..

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