Median, Interquartile Range, and Box Plots

Boxplots

Graphical Representation of the 5-number summary

​Boxplots show the "five number summary" of the data, dividing the data into quarters (25%). From the left to right on the diagram: Minimum, first quartile (Q1), Median (Q2), third quartile (Q3), and maximum. Outliers, if present, are shown as separate dots or asterisks.

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Definitions:

Minimum: The lowest value of the data set

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First Quartile (Q1): ​Middle of the lower half of the data set. 25% of the data lies below this value and 75% lies above.

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Median: Middle of the data set. Half the data (50%) lies below this value and half (50%) lies above. ​

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Third Quartile (Q3): Middle of the upper half of the data set. 75% of the data lies below this value and 25% lies above.​

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Maximum: The highest value of the data set.

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​Two additional pieces of information that can be determined are:

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The Interquartile Range (IQR) = Q3 - Q1

The Range = Max - Min​

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These pieces of information will show the extent to which the data is located near the center or near the extremes of the data set.​

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Measures of Spread

Match

Match the following terms with their definitions

• Minimum (Min)

• First Quartile (Q1)

• Median (Q2)

• Third Quartile (Q3)

• Maximum (Max)

The lowest value of the data set

Middle of the lower half of the data set. 25% of the data lies below this value and 75% lies above.

Middle of the data set. Half the data (50%) lies below this value and half (50%) lies above.

Middle of the upper half of the data set. 75% of the data lies below this value and 25% lies below.

The highest value of the data set

• The lowest value of the data set

• Middle of the lower half of the data set. 25% of the data lies below this value and 75% lies above.

• Middle of the data set. Half the data (50%) lies below this value and half (50%) lies above.

• Middle of the upper half of the data set. 75% of the data lies below this value and 25% lies below.

• The highest value of the data set

Match

Match the following visuals with their appropriate name?

Boxplot

Histogram

Dotplot

• Boxplot

• Histogram

• Dotplot