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Quintiles

Quintiles

The 20th and 80th percentiles of a set of data.

 

 

See also

Quartiles, deciles

Worked Example

Problem: Twenty students scored the following on a test (already sorted): 45, 50, 52, 55, 58, 60, 62, 65, 68, 70, 72, 74, 76, 78, 80, 82, 85, 88, 92, 95. Find the quintile boundaries that divide these scores into five equal groups.
Step 1: Since there are 20 data values, each quintile group contains 20 ÷ 5 = 4 values.
205=4 values per group\frac{20}{5} = 4 \text{ values per group}
Step 2: The 1st quintile boundary (Q₁, 20th percentile) falls between the 4th and 5th values. Average those two values.
Q1=55+582=56.5Q_1 = \frac{55 + 58}{2} = 56.5
Step 3: The 2nd quintile boundary (Q₂, 40th percentile) falls between the 8th and 9th values.
Q2=65+682=66.5Q_2 = \frac{65 + 68}{2} = 66.5
Step 4: The 3rd quintile boundary (Q₃, 60th percentile) falls between the 12th and 13th values.
Q3=74+762=75Q_3 = \frac{74 + 76}{2} = 75
Step 5: The 4th quintile boundary (Q₄, 80th percentile) falls between the 16th and 17th values.
Q4=82+852=83.5Q_4 = \frac{82 + 85}{2} = 83.5
Answer: The four quintile boundaries are 56.5, 66.5, 75, and 83.5. These divide the 20 scores into five groups of 4, with the lowest fifth scoring at or below 56.5 and the highest fifth scoring above 83.5.

Frequently Asked Questions

How many quintiles are there?
There are four quintile boundaries (at the 20th, 40th, 60th, and 80th percentiles) that create five quintile groups. People sometimes refer to the groups themselves as 'quintiles' — for example, 'the bottom quintile' means the lowest 20% of the data.
What is the difference between quintiles and quartiles?
Quartiles divide data into four equal parts (each containing 25% of the data), while quintiles divide data into five equal parts (each containing 20%). Quartiles use the 25th, 50th, and 75th percentiles; quintiles use the 20th, 40th, 60th, and 80th percentiles.

Quintiles vs. Quartiles

Quintiles split data into 5 equal groups of 20% each, using four cut points (20th, 40th, 60th, 80th percentiles). Quartiles split data into 4 equal groups of 25% each, using three cut points (25th, 50th, 75th percentiles). Both are specific types of quantiles — quintiles give a finer breakdown of the data than quartiles do.

Why It Matters

Quintiles are widely used in economics and public policy to analyze income distribution — you often hear phrases like 'the top quintile of earners' or 'the bottom quintile of households.' They also appear in standardized testing and health research to group populations into five equal-sized categories for comparison. Because each group represents exactly 20% of the data, quintiles provide a balanced and intuitive way to compare segments.

Common Mistakes

Mistake: Thinking there are five quintile values instead of four.
Correction: Four boundaries are needed to create five groups. The pattern is always one fewer boundary than the number of groups: quartiles have 3 boundaries for 4 groups, quintiles have 4 boundaries for 5 groups.
Mistake: Confusing a quintile boundary with a quintile group.
Correction: A quintile boundary is a specific data value (like the 20th percentile). A quintile group is the range of data between two consecutive boundaries. When someone says 'the third quintile,' clarify whether they mean the third cut point or the third group of data.

Related Terms