Quartiles Statistics Example 1

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

Example 1

easy
Find the quartiles (Q1Q_1, Q2Q_2, Q3Q_3) of the data set: 3, 5, 7, 8, 12, 14, 16, 18, 21.

Solution

  1. 1
    Step 1: The data is already sorted. There are 9 values, so Q2Q_2 (the median) is the 5th value: Q2=12Q_2 = 12.
  2. 2
    Step 2: The lower half is {3, 5, 7, 8}. Q1Q_1 is the median of this half: Q1=5+72=6Q_1 = \frac{5 + 7}{2} = 6.
  3. 3
    Step 3: The upper half is {14, 16, 18, 21}. Q3Q_3 is the median of this half: Q3=16+182=17Q_3 = \frac{16 + 18}{2} = 17.

Answer

Q1=6Q_1 = 6, Q2=12Q_2 = 12, Q3=17Q_3 = 17.
Quartiles divide sorted data into four equal parts. Q1Q_1 is the median of the lower half, Q2Q_2 is the overall median, and Q3Q_3 is the median of the upper half. Together they describe the spread and centre of the data.

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 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,

Example 4 hard

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

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