Five Number Summary

 

It consists of the following things:

• The minimum value of a data set is the least value in the set.
• The maximum value of a data set is the greatest value in the set.
• The range of a data set is the distance between the maximum and minimum value. To compute the range of a data set, we subtract the minimum from the maximum:
  range = maximum – minimum.
• The interquartile range of a data set is the distance between the two quartiles.
  Interquartile range = Q₃ – Q₁

_{It provides}  a way of determining the shape of the distribution .i.e. to see if there is symmetric or not in data.

For Symmetry:

a.     Difference between Second Quartile and Minimum Value is equal to difference between Maximum Value and Second Quartile (Q2-Xmin=Xmax-Q2)

b.     Difference between First Quartile and Minimum Value is equal to difference between Maximum value and Third quartile. (Q1-Xmin=Xmax-Q3)

For Right Skewed:

a.      Difference between Maximum value and Second quartile is greater than difference between Second Quartile and Minimum value. (Xmax-Q2>Q2-Xmin)

b.     Difference between Maximum value and Third Quartile is greater than First Quartile and Minimum Value. (Xmax-Q3>Q1-Xmin)

For Left Skewed

a.      Difference between Second Quartile and Minimum Value is greater than difference between Maximum value and Second Quartile. (Q2-Xmin>Xmax-Q2)

b.     Difference between First Quartile and Minimum Value is greater than difference between Maximum value and Third Quartile. (Q1-Xmin>Xmax-Q3)

Example 1:  Find the five-number summary for the data set {3, 7, 8, 5, 12, 14, 21, 13,

18}.

Minimum: 3         Q₁ : 6            Median: 12            Q₃ : 16           Maximum: 21

Example 2: Find the five-number summary for the data set {3, 7, 8, 5, 12, 14, 21, 15, 18, 14}.

Minimum: 3         Q₁ : 7            Median: 13            Q₃ : 15           Maximum: 21