Statistics Fundamentals • Topic 5 of 6

Quartiles

Quartiles split ordered data into four equal parts. The second quartile (Q2) is the median. The first quartile (Q1) is the median of the lower half, and the third quartile (Q3) is the median of the upper half. When the data has an odd count, the overall median is excluded from both halves before finding Q1 and Q3. About 25% of the data lies below Q1 and 75% below Q3. Quartiles underlie box plots and the interquartile range. On the SAT, the main skills are ordering the data and correctly splitting it into halves.

✅ Solved examples

1. Find Q1 of 2, 4, 6, 8, 10, 12.
Lower half is 2, 4, 6; its median is 4, so Q1 = 4.
2. Find Q3 of 2, 4, 6, 8, 10, 12.
Upper half is 8, 10, 12; its median is 10, so Q3 = 10.
3. Find the median (Q2) of 1, 3, 5, 7, 9.
The middle value is 5.
4. Find Q1 of 1, 2, 3, 4, 5, 6, 7, 8.
Lower half 1,2,3,4; median = (2 + 3)/2 = 2.5.

✏️ Practice — try these, take hints as needed

1. Find Q1 of 3, 6, 9, 12, 15, 18.
Lower half: 3, 6, 9.
Its median.
—
6.
2. Find Q3 of 3, 6, 9, 12, 15, 18.
Upper half: 12, 15, 18.
Its median.
—
15.
3. Find Q2 (median) of 2, 5, 8, 11, 14.
Middle of the ordered list.
—
—
8.
4. Find Q1 of 4, 8, 12, 16, 20, 24, 28, 32.
Lower half: 4, 8, 12, 16.
Average the middle two.
(8 + 12)/2.
10.
5. Find Q3 of 1, 2, 3, 4, 5, 6.
Upper half: 4, 5, 6.
Its median.
—
5.

📝 Topic test — 8 questions

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