Calculating Range and Quartiles

The five-number summary is another way to summarize data distribution. This summary contains the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value.

The minimum and maximum values define the extremes of the data set, indicating the lowest and highest values.

The quartiles divide the data into four equal parts. Q1 represents the 25th percentile, meaning 25% of the data falls below this value. Q2 is the median, representing the 50th percentile, meaning half of the data falls below this value and half the data falls above this value. Q3 represents the 75th percentile, with 75% of the data falling below it.

The range, calculated as the difference between the maximum and minimum values, provides a simple measure of the variability of the whole set of data. Another measure of variability is the interquartile range (IQR), which is the difference between Q3 and Q1. The IQR represents the range of the middle 50% of the data and is less affected by extreme values in the data.

Together, the five-number summary, range, and IQR provide information about the center and spread (variability) of a data set.