The data shown are the total compensation (in millions of...

The data shown are the total compensation (in millions of dollars) for the 50 top-paid CEOs for a recent year. Compare the averages, and state which one you think is the best measure. $$\begin{array}{lllll}17.5 & 18.0 & 36.8 & 31.7 & 31.7 \\17.3 & 24.3 & 47.7 & 38.5 & 17.0 \\23.7 & 16.5 & 25.1 & 17.4 & 18.0 \\37.6 & 19.7 & 21.4 & 28.6 & 21.6 \\19.3 & 20.0 & 16.9 & 25.2 & 19.8 \\25.0 & 17.2 & 20.4 & 20.1 & 29.1 \\19.1 & 25.2 & 23.2 & 25.9 & 24.0 \\41.7 & 24.0 & 16.8 & 26.8 & 31.4 \\16.9 & 17.2 & 24.1 & 35.2 & 19.1 \\22.9 & 18.2 & 25.4 & 35.4 & 25.5\end{array}$$

The data shown are the total compensation (in millions of dollars) for the 50 top-paid CEOs for a recent year. Compare the averages, and state which one you think is the best measure.
$$\begin{array}{lllll}17.5 & 18.0 & 36.8 & 31.7 & 31.7 \\17.3 & 24.3 & 47.7 & 38.5 & 17.0 \\23.7 & 16.5 & 25.1 & 17.4 & 18.0 \\37.6 & 19.7 & 21.4 & 28.6 & 21.6 \\19.3 & 20.0 & 16.9 & 25.2 & 19.8 \\25.0 & 17.2 & 20.4 & 20.1 & 29.1 \\19.1 & 25.2 & 23.2 & 25.9 & 24.0 \\41.7 & 24.0 & 16.8 & 26.8 & 31.4 \\16.9 & 17.2 & 24.1 & 35.2 & 19.1 \\22.9 & 18.2 & 25.4 & 35.4 & 25.5\end{array}$$

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Key Concepts

Central Tendency

Central tendency refers to the statistical measures that describe the center or typical value of a dataset. These measures, which include the mean and median, provide a summary of the data by identifying a single value that represents a set of observations.

Mean

The mean is the arithmetic average of a dataset, computed by summing all values and dividing by the number of observations. It is widely used for its simplicity, but it can be heavily influenced by extreme values or outliers, which might distort the true central location of the data.

Median

The median is the middle value in an ordered dataset, dividing the data into two equal halves. It is less affected by outliers and skewed data than the mean, making it a more robust measure of central tendency when the dataset contains extreme values or is not symmetrically distributed.

Outliers

Outliers are data points that are significantly higher or lower than the majority of the data. Their presence can skew the mean, making it less representative of the dataset as a whole, while the median remains relatively unaffected, thereby often serving as a better measure of the typical value in such situations.

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