Measures of spread

Topic summary

Measures of Spread

Measures of spread indicate how much variation or dispersion exists in a data set. Understanding the spread is crucial for interpreting data and assessing its reliability. The most common measures of spread are:

Range

The range is the simplest measure of spread, calculated as the difference between the maximum and minimum values in a data set:

\[\text{Range} = \text{Maximum} – \text{Minimum}\]

For example, if the data set is \(\{3, 7, 5, 10, 2\}\), the range is:

\[\text{Range} = 10 – 2 = 8\]

Interquartile range (IQR)

The IQR measures the spread of the middle 50% of the data by calculating the difference between the upper quartile \(Q_3\) and the lower quartile \(Q_1\):

\[\text{IQR} = Q_3 – Q_1\]

The IQR is less affected by outliers compared to the range, making it a better measure of spread for skewed distributions.

Interpercentile range

The interpercentile range measures the spread between two specified percentiles. For instance, the interpercentile range between the \(p\)-th percentile and the \(q\)-th percentile is calculated as:

\[\text{Interpercentile range} = P_q – P_p\]

Where \(P_q\) and \(P_p\) are the values at the \(q\)-th and \(p\)-th percentiles, respectively. This measure is useful for understanding the spread of data in relation to specific percentiles.