Box Plot Math Example 3

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Example 3

easy
A box plot shows: minimum=10, Q1=25Q_1=25, median=40, Q3=55Q_3=55, maximum=70. Calculate the IQR and determine the fence values for outlier detection.

Solution

  1. 1
    IQR =Q3−Q1=55−25=30= Q_3 - Q_1 = 55 - 25 = 30
  2. 2
    Lower fence =Q1−1.5×IQR=25−45=−20= Q_1 - 1.5 \times IQR = 25 - 45 = -20
  3. 3
    Upper fence =Q3+1.5×IQR=55+45=100= Q_3 + 1.5 \times IQR = 55 + 45 = 100

Answer

IQR = 30; Lower fence = -20; Upper fence = 100.
The fences define the boundary for outlier detection. Since the minimum (10) exceeds -20 and the maximum (70) is below 100, there are no outliers in this data set. Both whiskers extend to the actual data extremes.

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 4 hard

A data set has [formula], [formula], and a suspected outlier at value 60. Determine whether 60 is tr

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