Quartiles Math Example 3

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Example 3

medium
Find Q1Q_1, Q2Q_2, and Q3Q_3 for the dataset: 4,7,8,12,15,18,21,25,304, 7, 8, 12, 15, 18, 21, 25, 30.

Solution

  1. 1
    The data is already sorted and n=9n = 9 (odd). The median Q2Q_2 is the middle value at position 9+12=5\frac{9+1}{2} = 5: Q2=15Q_2 = 15.
  2. 2
    Lower half (exclude median): {4,7,8,12}\{4, 7, 8, 12\}. With 4 values, Q1=7+82=7.5Q_1 = \frac{7 + 8}{2} = 7.5.
  3. 3
    Upper half (exclude median): {18,21,25,30}\{18, 21, 25, 30\}. With 4 values, Q3=21+252=23Q_3 = \frac{21 + 25}{2} = 23.

Answer

Q1=7.5,  Q2=15,  Q3=23Q_1 = 7.5,\; Q_2 = 15,\; Q_3 = 23
For an odd-sized dataset, the median is the central value. Exclude the median, then find the median of each half. When a half has an even count, average the two middle values. The IQR would be Q3−Q1=23−7.5=15.5Q_3 - Q_1 = 23 - 7.5 = 15.5.

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 2 medium

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

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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