Box Plot Statistics Example 2

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Example 2

medium
A box plot shows: Min = 10, Q1 = 20, Median = 35, Q3 = 50, Max = 90. Calculate the IQR and determine if a value of 100 would be an outlier using the 1.5×IQR rule.

Solution

  1. 1
    Step 1: IQR = Q3−Q1=50−20=30Q3 - Q1 = 50 - 20 = 30.
  2. 2
    Step 2: Upper fence = Q3+1.5×IQR=50+45=95Q3 + 1.5 \times \text{IQR} = 50 + 45 = 95.
  3. 3
    Step 3: Since 100 > 95, it would be classified as an outlier.

Answer

IQR = 30. Yes, 100 is an outlier (above the upper fence of 95).
The 1.5×IQR rule provides a systematic way to identify outliers. Any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is considered an outlier.

About Box Plot

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

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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 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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