Box Plot Statistics Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

medium
Data: 2, 4, 5, 7, 8, 9, 11, 13, 15. Find the five-number summary and describe how to draw a box plot.

Solution

  1. 1
    Step 1: Minimum = 2, Maximum = 15, Median (Q2) = 8 (5th of 9 values).
  2. 2
    Step 2: Lower half: {2, 4, 5, 7}. Q1 = 4+52=4.5\frac{4+5}{2} = 4.5.
  3. 3
    Step 3: Upper half: {9, 11, 13, 15}. Q3 = 11+132=12\frac{11+13}{2} = 12. Draw a box from Q1 (4.5) to Q3 (12), line at median (8), whiskers to min (2) and max (15).

Answer

Five-number summary: Min = 2, Q1 = 4.5, Median = 8, Q3 = 12, Max = 15.
A box plot (box-and-whisker plot) visualises the five-number summary, showing the spread and centre of the data. The interquartile range (IQR = Q3 − Q1) shows where the middle 50% of data lies.

About Box Plot

A visual display of the five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

Learn more about Box Plot →

More Box Plot Examples

Example 2 medium

A box plot shows: Min = 10, Q1 = 20, Median = 35, Q3 = 50, Max = 90. Calculate the IQR and determine

Example 3 medium

Data: 3, 5, 6, 8, 10, 12, 14. Find the five-number summary.

Example 4 medium

A box plot has Min = 4, Q1 = 9, Median = 12, Q3 = 18, Max = 21. Find the interquartile range and sta

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