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1.7 Summary Statistics for a Quantitative Variable

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Measures of Center: Mean and Median

Two key measures summarize the center of a distribution:

Mean

\bar{x} = \frac{\sum x_i}{n} = \frac{x_1 + x_2 + \cdots + x_n}{n}

Where ${\bar{x}}$ (read "x-bar") is the sample mean and ${n}$ is the number of observations.

Median

If ${n}$ is odd: median = middle value
If ${n}$ is even: median = average of the two middle values

\text{position of median} = \frac{n+1}{2}

Which to use?

Symmetric distributions → mean and median are similar; either works
Skewed distributions → median is preferred (resistant to outliers)
Distributions with outliers → median is preferred

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