Quartiles Statistics Example 3

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

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, 50. Find Q1Q_1, Q2Q_2, and Q3Q_3, and determine how many members are between Q1Q_1 and Q3Q_3.

Solution

  1. 1
    Step 1: 15 values, so Q2Q_2 = 8th value = 25. Lower half: {18,19,20,21,22,23,24}, Q1Q_1 = 4th value = 21. Upper half: {27,30,32,35,40,45,50}, Q3Q_3 = 4th value = 35.
  2. 2
    Step 2: Members between Q1=21Q_1=21 and Q3=35Q_3=35 (inclusive): 21,22,23,24,25,27,30,32,35 = 9 members. This is approximately 60% of the data, close to the expected 50% within the IQR.

Answer

Q1=21Q_1 = 21, Q2=25Q_2 = 25, Q3=35Q_3 = 35. Nine members (60%) have ages between Q1Q_1 and Q3Q_3 inclusive.
By definition, approximately 50% of data falls between Q1Q_1 and Q3Q_3 (the interquartile range). The exact count depends on how boundary values are handled and whether the data set size is large enough for the quartiles to split it evenly.

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 4 hard

Two data sets have the same median ([formula]). Data set A: [formula], [formula]. Data set B: [formu

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