Box Plot Math Example 1

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

Example 1

medium
For the data set {3,7,8,10,12,14,18,20,25,100}\{3, 7, 8, 10, 12, 14, 18, 20, 25, 100\}, construct a box plot and identify any outliers using the 1.5×IQR1.5 \times IQR rule.

Solution

  1. 1
    Order the data (already ordered). Find quartiles: Q1=8Q_1 = 8 (median of lower half {3,7,8,10,12}\{3,7,8,10,12\}... median is 8), Q2=13Q_2 = 13 (average of 12 and 14), Q3=20Q_3 = 20 (median of upper half {14,18,20,25,100}\{14,18,20,25,100\}... median is 20)
  2. 2
    Calculate IQR: IQR=Q3−Q1=20−8=12IQR = Q_3 - Q_1 = 20 - 8 = 12
  3. 3
    Find fences: Lower fence =Q1−1.5×IQR=8−18=−10= Q_1 - 1.5 \times IQR = 8 - 18 = -10; Upper fence =Q3+1.5×IQR=20+18=38= Q_3 + 1.5 \times IQR = 20 + 18 = 38
  4. 4
    Identify outliers: any value below −10-10 or above 3838. The value 100 exceeds 38, so it is an outlier
  5. 5
    Draw box plot: whiskers extend to 3 (min non-outlier) and 25 (max non-outlier); box from Q1=8Q_1=8 to Q3=20Q_3=20; line at median Q2=13Q_2=13; plot 100 as a separate dot

Answer

100 is an outlier (exceeds upper fence of 38). Whiskers: [3, 25]. Box: [8, 20]. Median: 13.
The 1.5×IQR rule identifies potential outliers by establishing fences beyond which data is unusual. Box plots provide a five-number summary (min, Q1, median, Q3, max) while flagging extreme values as separate dots.

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 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

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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