The data shown represent the number of runs made each year...

The data shown represent the number of runs made each year during Bill Mazeroski's career. Check for normality.
$$
\begin{array}{llllllllllll}
30 & 59 & 69 & 50 & 58 & 71 & 55 & 43 & 66 & 52 & 56 & 62 \\
36 & 13 & 29 & 17 & 3 & & & & & & &
\end{array}
$$

Key Concepts

Statistical Tests for Normality

Various formal tests, such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test, are used to statistically assess normality. These tests provide a p-value that helps determine if the observed distribution significantly departs from a normal distribution, guiding the selection of appropriate statistical methods.

Data Skewness and Kurtosis

Skewness measures the asymmetry of the data distribution, while kurtosis indicates the 'tailedness' relative to a normal distribution. These numerical indicators help in understanding the shape of the data distribution and identifying departures from normality, supplementing both graphical and statistical tests.

Graphical Methods for Assessing Normality

Graphical tools such as histograms and Q-Q (quantile-quantile) plots are common techniques to visually inspect whether data approximate a normal distribution. A histogram provides a visual representation of data frequency, while a Q-Q plot compares the quantiles of the sample data against those of a normal distribution to identify deviations from normality.

Normal Distribution

This concept refers to a probability distribution that is symmetric about its mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In statistical analysis, many procedures assume the data are normally distributed, which emphasizes the importance of verifying normality before applying these methods.

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