Summary
Highlights
The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. This summary is used to construct a box plot. To begin, the data set must be ordered from least to greatest.
For an example dataset, the minimum is 0 and the maximum is 10. The median is the middle number; for an even dataset, it's the average of the two middle numbers (e.g., 3.5 for 3 and 4). To find Q1 and Q3, split the data into lower and upper halves. Q1 is the median of the lower half (e.g., 2), and Q3 is the median of the upper half (e.g., 5).
To construct a box plot, use a number line ranging from the minimum to the maximum. Draw vertical lines for the minimum, maximum, median, Q1, and Q3. Create a box between Q1 and Q3, with the median inside. The width of this box represents the interquartile range (IQR). 'Whiskers' extend from the box to the minimum and maximum values.
A modified box plot can identify outliers. An outlier is a value less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR. In the example, the IQR is 3. The lower fence is -2.5 (no lower outliers), and the upper fence is 9.5, making 10 an upper outlier. On a modified box plot, the whisker extends to the maximum non-outlier, and outliers are marked with a dot.