Box Plot Statistics Example 4

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

Example 4

medium
A box plot has Min = 4, Q1 = 9, Median = 12, Q3 = 18, Max = 21. Find the interquartile range and state the interval containing the middle 50% of the data.

Solution

  1. 1
    Step 1: The interquartile range is Q3−Q1=18−9=9Q3 - Q1 = 18 - 9 = 9.
  2. 2
    Step 2: The middle 50% of the data lies between Q1=9Q1 = 9 and Q3=18Q3 = 18.

Answer

IQR = 99, and the middle 50% lies from 99 to 1818.
The box in a box plot represents the middle half of the data. The interquartile range measures the spread of that middle 50%, making it a useful summary of variability.

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 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

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.

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