Ch. 2 - Exploring Data with Tables and Graphs

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 2 - Exploring Data with Tables and Graphs

Problem 2.2.4

Chapter 2, Problem 2.2.4

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

Textbook Question

In Exercises 13 and 14, construct the pie chart.

Box Office Boffo Use the data from Exercise 11 “Box Office Boffo.”

"Recent annual gross revenue (millions of dollars) for the leading movie studios are as follows: 20th Century Fox (1082), Buena Vista (3092), Paramount (757), Sony/Columbia (1304), Universal (1772), Warner Brothers (1941)."

Textbook Question

Exercises 29–34 involve large sets of data, so technology should be used. Complete lists of the data are not listed in Appendix B, but they can be downloaded from the website TriolaStats.com. Use the indicated data and construct the frequency distribution.

Earthquake Depths Use the depths (km) of the 600 earthquakes included in Data Set 24 “Earthquakes.” Use a class width of 10.0 km and begin with a lower class limit of 0.0 km. Does the frequency distribution appear to be a normal distribution?

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Textbook Question

Airport Data Speeds Listed below are the cellular data speeds (Mbps) from Sprint and Verizon measured at nine different airports (based on data from CNN). What would the presence of a correlation suggest about Sprint and Verizon?

Textbook Question

V and Digital Ads Listed below are amounts (billions of dollars) spent on TV and digital advertising. The amounts are listed in order by year ending with the year 2022. The last few years are projected amounts (based on data from Magna Global). Construct a graph that reveals the story that the data are trying to tell. What story does the graph depict?

TV Ads:

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Textbook Question

Ethics There are data showing that smoking is detrimental to good health. Given that people could be helped and lives could be saved by reducing smoking, is it ethical to graph the data in a way that is misleading by exaggerating the health risks of smoking?

Textbook Question

In Exercises 13–16, write a statement that interprets the P-value and includes a conclusion about linear correlation.

Using the data from Exercise 6 “Airport Data Speeds,” the P-value is 0.003.