Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

2. Describing Data with Tables and Graphs

Histograms

Statistics

2. Describing Data with Tables and Graphs

Histograms

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2:39 minutes

Problem 2.2.4

Textbook Question

Cell Phone Radiation If we collect a sample of cell phone radiation amounts much larger than the sample included with Exercise 3, and if our sample includes a single outlier, how will that outlier appear in a histogram?

Verified step by step guidance

Understand the concept of an outlier: An outlier is a data point that is significantly different from the other data points in a dataset. It can be much higher or lower than the rest of the data.

Consider the effect of an outlier on a histogram: A histogram is a graphical representation of the distribution of numerical data. It shows the frequency of data points within specified ranges (bins). An outlier will appear as a bar that is separate from the other bars, often at the far end of the histogram.

Visualize the histogram: Imagine the histogram of cell phone radiation amounts. Most data points will cluster around a central range, forming a series of bars. The outlier will be a single bar that is distant from the cluster, indicating its rarity and extremity.

Analyze the impact on the histogram shape: The presence of an outlier can skew the histogram, making it asymmetrical. If the outlier is much larger than the other values, it will extend the range of the histogram, potentially creating a long tail on one side.

Consider the implications for data interpretation: The outlier can affect statistical measures such as the mean and standard deviation, making them less representative of the central tendency of the data. It's important to identify and consider outliers when analyzing data distributions.

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Key Concepts

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

Outliers

An outlier is a data point that significantly differs from other observations in a dataset. It can skew the results and affect the overall analysis. In a histogram, an outlier will appear as a bar that is isolated from the rest of the data, often at the extreme end of the distribution.

Histograms

A histogram is a graphical representation of the distribution of numerical data, where data is grouped into bins or intervals. Each bar in a histogram represents the frequency of data points within each bin. It helps in visualizing the shape, spread, and central tendency of the data.

Sample Size

Sample size refers to the number of observations or data points collected in a study. A larger sample size can provide more reliable and accurate estimates of the population parameters. It also affects the visibility and impact of outliers in a histogram, as a larger sample may dilute the effect of an outlier.

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Related Practice

Multiple Choice

Use the frequency histogram below to determine (a) the number of classes and (b) the class width.

Textbook Question

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

Burger King Dinner Service Times Use the frequency distribution from Exercise 18 in Section 2-1 to construct a histogram. Using a strict interpretation of the criteria for being a normal distribution, does the histogram appear to depict data from a population with a normal distribution?

Textbook Question

IQ Scores IQ scores of adults are normally distributed. If a large sample of adults is randomly selected and the IQ scores are illustrated in a histogram, what is the shape of that histogram?

Textbook Question

More IQ Scores The population of IQ scores of adults is normally distributed. If we obtain a voluntary response sample of 5000 of those IQ scores, will a histogram of the sample be bell-shaped?

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?

Textbook Question

Class Width and Class Limits Give the approximate values of the class width, and the lower and upper class limits of the class depicted in the bar farthest to the left.

Textbook Question

Relative Frequency Histogram How would the shape of the histogram change if the vertical scale uses relative frequencies expressed in percentages instead of the actual frequency counts as shown here?

Textbook Question

Interpreting a Graph The accompanying graph plots the numbers of points scored in each Super Bowl from the first Super Bowl in 1967 (coded as year 1) to the last Super Bowl at the time of this writing. The graph of the quadratic equation that best fits the data is also shown in red. What feature of the graph justifies the value of R^2 = 0.205 for the quadratic model?

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