Quartiles Statistics Example 2

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

Example 2

medium
Find the quartiles of this data set with an even number of values: 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65.

Solution

  1. 1
    Step 1: There are 12 values. Q2Q_2 = median = average of 6th and 7th values: Q2=35+402=37.5Q_2 = \frac{35 + 40}{2} = 37.5.
  2. 2
    Step 2: Lower half: {10, 15, 20, 25, 30, 35}. Q1Q_1 = median = 20+252=22.5\frac{20 + 25}{2} = 22.5.
  3. 3
    Step 3: Upper half: {40, 45, 50, 55, 60, 65}. Q3Q_3 = median = 50+552=52.5\frac{50 + 55}{2} = 52.5.

Answer

Q1=22.5Q_1 = 22.5, Q2=37.5Q_2 = 37.5, Q3=52.5Q_3 = 52.5.
When the data set has an even number of values, the median is the average of the two middle values. The lower and upper halves each contain half the data, and their medians give Q1Q_1 and Q3Q_3 respectively.

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 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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