Box Plot Math Example 4

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

Example 4

hard
A data set has Q1=20Q_1 = 20, Q3=35Q_3 = 35, and a suspected outlier at value 60. Determine whether 60 is truly an outlier using the 1.5×IQR1.5 \times IQR rule, and explain how removing it would affect the box plot.

Solution

  1. 1
    Calculate IQR: IQR=Q3−Q1=35−20=15IQR = Q_3 - Q_1 = 35 - 20 = 15
  2. 2
    Calculate upper fence: Q3+1.5×IQR=35+22.5=57.5Q_3 + 1.5 \times IQR = 35 + 22.5 = 57.5
  3. 3
    Compare: 60 > 57.5, so yes, 60 is classified as an outlier
  4. 4
    Effect of removal: the upper whisker would shorten, the box dimensions (Q1,Q3Q_1, Q_3) might shift slightly, and the maximum displayed would decrease

Answer

60 is an outlier (exceeds upper fence of 57.5). Removing it shortens the upper whisker.
Outliers appear as isolated dots beyond the whiskers in a box plot. Their removal changes the scale and whisker length but not the box itself (if Q1 and Q3 are unaffected). Always investigate outliers rather than automatically removing them.

About Box Plot

A box plot displays the five-number summary (minimum, Q1, median, Q3, maximum) of a data set using a box and whiskers.

Learn more about Box Plot →

More Box Plot Examples

Example 1 medium

For the data set [formula], construct a box plot and identify any outliers using the [formula] rule.

Example 2 medium

Two box plots compare exam scores for two classes. Class A: median=72, [formula], [formula]. Class B

Example 3 easy

A box plot shows: minimum=10, [formula], median=40, [formula], maximum=70. Calculate the IQR and det

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