Quartiles Math Example 2

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

Example 2

medium
A dataset of 10 values (sorted): {2,5,8,12,15,18,21,25,30,40}\{2, 5, 8, 12, 15, 18, 21, 25, 30, 40\}. Find all quartiles and the five-number summary.

Solution

  1. 1
    Q2Q_2: with n=10n=10 (even), median =15+182=16.5= \frac{15+18}{2} = 16.5
  2. 2
    Lower half: {2,5,8,12,15}\{2, 5, 8, 12, 15\}; Q1=8Q_1 = 8 (middle value)
  3. 3
    Upper half: {18,21,25,30,40}\{18, 21, 25, 30, 40\}; Q3=25Q_3 = 25 (middle value)
  4. 4
    Five-number summary: Min=2, Q1=8Q_1=8, Q2=16.5Q_2=16.5, Q3=25Q_3=25, Max=40

Answer

Five-number summary: {2,8,16.5,25,40}\{2, 8, 16.5, 25, 40\}
The five-number summary (min, Q1, median, Q3, max) provides a complete picture of distribution. It forms the basis for box plots and is resistant to outliers, making it ideal for describing skewed data.

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 1 easy

Find the quartiles [formula], [formula], and [formula] for the data set: [formula].

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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