Descriptive Statistics

Sample variance

Average squared deviation using n - 1 in the denominator.

$$s^2 = \frac{1}{n-1}\sum (x_i - \bar{x})^2$$

• Mean $\bar{x} = \frac{\sum x_i}{n}$.
• Sample standard deviation: $s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}$.
• IQR $= Q_3 - Q_1$; outliers fall more than $1.5 \times$ IQR beyond the quartiles.
• A long right tail pulls the mean above the median.

• Finding the median without sorting the data first.
• Using $n$ instead of $n - 1$ for a sample standard deviation.
• Reporting the mean for strongly skewed data without comment.

Try each one, then open the answer. Numerical answers on this page are verified by an automated calculation check.

1. 1.Find the mean of $4, 8, 15, 16, 23, 42$.

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   $18$

2. 2.Find the median of $12, 5, 9, 20, 7, 14$.

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   $10.5$

3. 3.Find the population standard deviation of $2, 4, 4, 4, 5, 5, 7, 9$.

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   $2$

• The Normal Distribution
• Confidence Intervals
• All Introductory Statistics topics