Use the Empirical Rule. The monthly utility bills for eight...

Use the Empirical Rule. The monthly utility bills for eight more households are listed. Using the sample statistics from Exercise $30,$ determine which of the data entries are unusual. Are any of the data entries very unusual? Explain your reasoning. $\$ 65, \$ 52, \$ 63, \$ 83, \$ 77, \$ 98, \$ 84, \$ 70$

Use the Empirical Rule.
The monthly utility bills for eight more households are listed. Using the sample statistics from Exercise $30,$ determine which of the data entries are unusual. Are any of the data entries very unusual? Explain your reasoning.
$\$ 65, \$ 52, \$ 63, \$ 83, \$ 77, \$ 98, \$ 84, \$ 70$

Key Concepts

Normal Distribution

A normal distribution is a symmetric, bell-shaped distribution where most observations cluster around the mean. Many statistical methods, including the application of the Empirical Rule, assume data follows this distribution, which is essential for determining the probability of extreme values and fitting the criteria for unusual data points.

Outliers

Outliers are data points that deviate significantly from the overall pattern of a dataset. In the context of the Empirical Rule, observations lying more than two or three standard deviations from the mean are typically considered unusual or very unusual. Identifying outliers is crucial for understanding the variability in data and for further statistical analysis.

Empirical Rule

The Empirical Rule states that for a normally distributed dataset, approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and nearly 99.7% falls within three standard deviations. This rule allows us to assess the spread of the data and identify which observations are typical versus those that are unusual.

Sample Statistics

Sample statistics, such as the sample mean and sample standard deviation, summarize the central tendency and variability of a dataset, respectively. They provide the necessary parameters to apply the Empirical Rule, which in turn helps in judging whether individual data entries are typical or unusual within the context of the sample.

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