Box Plot Math Example 2

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

Example 2

medium
Two box plots compare exam scores for two classes. Class A: median=72, Q1=65Q_1=65, Q3=80Q_3=80. Class B: median=78, Q1=70Q_1=70, Q3=85Q_3=85. Compare center and spread for both classes.

Solution

  1. 1
    Compare centers (medians): Class B has higher median (78 > 72), suggesting Class B typically scores higher
  2. 2
    Calculate IQRs: IQRA=80−65=15IQR_A = 80-65=15; IQRB=85−70=15IQR_B = 85-70=15
  3. 3
    Compare spread: Both classes have equal IQR of 15, meaning similar variability in the middle 50% of scores
  4. 4
    Conclusion: Class B performs better on average (higher center), but both classes show the same spread

Answer

Class B has a higher center (median=78 vs 72). Both have equal spread (IQR=15).
Box plots enable side-by-side comparison of distributions. Center comparison uses medians; spread comparison uses IQR. Unlike means and standard deviations, these measures are resistant to outliers.

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 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

← All Box Plot Examples Box Plot Concept