The five number summary is a descriptive statistic which provide information about a set of observation. The quartiles aids us to understand the spread of the data set given. The five number summary is useful to compare various set of observations which is then represented through the boxplot. Five number summary, consists of

  • Minimum
  • Maximum
  • Median
  • First quartile, and
  • Third quartile.

Generally a computer is used to calculate the five number summary. Given below are the few steps which will help you understand how it is calculated:
Step 1: The given data should be arranged from the smallest value to the largest value which is on the left and right respectively.

Step 2: Find the minimum and the maximum value from the given data.

Step 3: Median gives the middle number, if it is an even number then the median is the mean of the two middle numbers.

Step 4: Upper Quartile (Q3): It is the median of the upper half of the given data set $\frac{3}{4}$$(n+1)$ nth value where n is the number of data values in the data set.

Step 5: Lower Quartile (Q1): It is the median of the lower half of the given data set $\frac{1}{4}$$(n+1)$ nth value where n is the number of data values in the data set.