Statistics (Measures of Center & Variability) • Topic 3 of 4

Box Plots — Five-Number Summary

A box plot displays data distribution using five key values:

Value	Meaning
Minimum	Smallest value in the dataset
Q1	First quartile — median of the lower half (25th percentile)
Median (Q2)	Middle value (50th percentile)
Q3	Third quartile — median of the upper half (75th percentile)
Maximum	Largest value in the dataset

Interquartile Range (IQR) = Q3 - Q1. This represents the spread of the middle 50% of data and is resistant to outliers.

BOX PLOT ANATOMY:

  Min   Q1   Median  Q3   Max
   2     4      6     12    15
   |     |      |      |     |
   |-----|======|======|-----|
          (box = IQR)

  IQR = Q3 - Q1 = 12 - 4 = 8
  Range = Max - Min = 15 - 2 = 13

Box contains middle 50% of data.
Whiskers extend to Min and Max.

Solved Examples

Worked Example

Find five-number summary for {5, 7, 8, 12, 15, 18, 21}.

SolutionMin=5, Q1=7 (lower half 5,7,8 -> median=7), Median=12, Q3=18 (upper half 15,18,21 -> median=18), Max=21. IQR=18-7=11.

Worked Example

Find IQR and range: Q1=25, Q3=75, Min=10, Max=100.

SolutionIQR = 75 - 25 = 50. Range = 100 - 10 = 90.

Key Points

Box plot shows distribution without listing all data points
IQR = Q3 - Q1 (middle 50% spread, resistant to outliers)
Longer box = more spread in the middle 50%
Compare two box plots: look at medians, IQR, and overall range

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The five-number summary is minimum, Q1, median, Q3, and:

Explanation: Maximum.

Q2.The interquartile range (IQR) is:

Explanation: $Q_3-Q_1$.

Q3.The box of a box plot spans:

Explanation: $Q_1$ to $Q_3$.

Q4.The whiskers reach the:

Explanation: Min and max.

Practice more MCQs → 📝 Assignment · 35 marks