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Decisions Through Data Home


Statistics: Decisions Through Data

UNIT 5: Boxplots

Summary of the Video

How many calories does a hot dog contain? The calorie count varies with the type of hot dog and also from brand to brand. We see a tester analyzing hot dogs, and note that center alone is not an adequate numerical description of a distribution. We need a measure of spread or variability as well.

A stemplot of the calorie content of 20 brands of beef hot dogs appears. We find the median to describe the center. The quartiles are the one-quarter and three-quarter points in the ordered observations, just as the median is the midpoint. The video describes the rule for finding the quartiles. The quartiles help indicate spread. Even better is the five-number summary , consisting of the median, the two quartiles, and the smallest and largest individual observations. We can see spread (how far apart are the quartiles and the extremes) and we can also see the unequal spread of the two sides of a skewed distribution (how far are the quartiles and the extremes from the median).

The boxplot is a graph of the five-number summary. The box spans the quartiles, the median is marked inside the box, and whiskers extend out to the extremes. Boxplots don't show a distribution in detail, as a comparison of boxplot and stemplot for calories in beef hot dogs illustrates. However, boxplots are useful for comparing several distributions. Boxplots of calories in beef, meat, and poultry hot dogs (the government's three allowed types) show that poultry franks as a group have markedly fewer calories.


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