The Five Number Summary is a statistical method used to describe a dataset using five important values. It provides a quick overview of the distribution, center, and spread of the data.
The five values included in a Five Number Summary are
- Minimum Value – The smallest value in the dataset.
- First Quartile (Q1) – The middle value of the lower half of the dataset.
- Median (Q2) – The middle value of the entire dataset.
- Third Quartile (Q3) – The middle value of the upper half of the dataset.
- Maximum Value – The largest value in the dataset.
Steps to Calculate the Five-Number Summary
1. Arrange the data in ascending order.
2. Find the Minimum Value: The smallest value in the dataset.
3. Find the Maximum Value: The largest value in the dataset.
4. Find the Median (Q2)
- Position of Median = (n + 1) / 2
- The value at this position is the median.
5. Find the First Quartile (Q1)
- Position of Q1 = (n + 1) / 4
- The value at this position is the first quartile.
6. Find the Third Quartile (Q3)
- Position of Q3 = 3(n + 1) / 4
- The value at this position is the third quartile.
- n = Total number of observations in the dataset.
This gives the five values: Minimum Value, Q1, Median (Q2), Q3, and Maximum Value.
Uses of Five-Number Summary
- Provides a concise summary of a dataset.
- Helps understand the distribution and spread of data.
- Assists in identifying outliers.
- Forms the basis of a box-and-whisker plot (box plot).
- Makes comparison between datasets easier.
➢Practice: Solved Examples