Quartiles Math Example 4

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

Example 4

easy
Find Q1Q_1 and Q3Q_3 for: {10,20,30,40,50,60,70}\{10, 20, 30, 40, 50, 60, 70\}.

Solution

  1. 1
    n=7n = 7; Q2=40Q_2 = 40 (middle value at position 4)
  2. 2
    Lower half: {10,20,30}\{10, 20, 30\}; Q1=20Q_1 = 20
  3. 3
    Upper half: {50,60,70}\{50, 60, 70\}; Q3=60Q_3 = 60

Answer

Q1=20Q_1 = 20, Q3=60Q_3 = 60
When nn is odd, exclude the median from both halves before finding Q1 and Q3. Each half contains (n−1)/2(n-1)/2 values. Here each half has 3 values, and the middle value of each is the quartile.

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 3 medium

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

Example 5 hard

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

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