Quartiles Math 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, and Q3Q_3 for the data set: {4,7,9,11,14,18,22,25,30}\{4, 7, 9, 11, 14, 18, 22, 25, 30\}.

Solution

  1. 1
    The data is already sorted; n=9n = 9
  2. 2
    Q2Q_2 (median): middle value at position 5 → Q2=14Q_2 = 14
  3. 3
    Lower half (below median): {4,7,9,11}\{4, 7, 9, 11\}; Q1Q_1 = median of lower half =7+92=8= \frac{7+9}{2} = 8
  4. 4
    Upper half (above median): {18,22,25,30}\{18, 22, 25, 30\}; Q3Q_3 = median of upper half =22+252=23.5= \frac{22+25}{2} = 23.5

Answer

Q1=8Q_1 = 8, Q2=14Q_2 = 14, Q3=23.5Q_3 = 23.5
Quartiles divide ordered data into four equal parts. Q1 is the 25th percentile, Q2 (median) is the 50th percentile, and Q3 is the 75th percentile. For even-sized halves, average the two middle values.

About Quartiles

Quartiles divide an ordered data set into four equal parts: Q1 is the 25th percentile, Q2 is the median (50th), and Q3 is the 75th percentile.

Learn more about Quartiles →

More Quartiles Examples

Example 2 medium

A dataset of 10 values (sorted): [formula]. Find all quartiles and the five-number summary.

Example 3 medium

Find [formula], [formula], and [formula] for the dataset: [formula].

Example 4 easy

Find [formula] and [formula] for: [formula].

Example 5 hard

A student scores at the 75th percentile on a standardized test with scores [formula]. Confirm that [

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