Quartiles Statistics Example 4

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

Example 4

hard
Two data sets have the same median (Q2=50Q_2 = 50). Data set A: Q1=45Q_1 = 45, Q3=55Q_3 = 55. Data set B: Q1=20Q_1 = 20, Q3=80Q_3 = 80. Compare the distributions and explain what the quartiles reveal about each data set.

Solution

  1. 1
    Step 1: Data set A: IQR = 55−45=1055 - 45 = 10. The middle 50% of values are within 5 units of the median. Data set B: IQR = 80−20=6080 - 20 = 60. The middle 50% of values span 60 units.
  2. 2
    Step 2: Data set A is tightly clustered around the median with low variability. Data set B is widely spread with high variability. Despite identical medians, the distributions are very different — A is consistent while B has extreme variation.

Answer

Both share a median of 50, but A (IQR=10) is tightly clustered while B (IQR=60) is widely spread. Quartiles reveal that A's data is much more consistent than B's.
Quartiles provide more information than the median alone. The spread between Q1Q_1 and Q3Q_3 (the IQR) measures the variability of the middle 50% of the data. Two distributions with the same median can have vastly different spreads, which quartiles help quantify.

About Quartiles

Quartiles are values that divide ordered data into four equal parts: Q1Q_1 (25th percentile) marks the boundary below which 25% of data falls, Q2Q_2 (the median, 50th percentile) splits the data in half, and Q3Q_3 (75th percentile) marks the boundary below which 75% falls.

Learn more about Quartiles →

More Quartiles Examples

Example 1 easy

Find the quartiles ([formula], [formula], [formula]) of the data set: 3, 5, 7, 8, 12, 14, 16, 18, 21

Example 2 medium

Find the quartiles of this data set with an even number of values: 10, 15, 20, 25, 30, 35, 40, 45, 5

Example 3 medium

The ages of 15 members of a sports club are: 18, 19, 20, 21, 22, 23, 24, 25, 27, 30, 32, 35, 40, 45,

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