Decile: Definition, Calculation, and Uses
What is a decile?
A decile is a quantile that divides a ranked dataset into 10 equal parts. Each decile point (D1 through D9) corresponds to a value below which a fixed percentage of observations fall:
– D1: 10% of observations are below this value
– D2: 20% below
– …
– D9: 90% below
Decile ranks label observations on a 1–10 scale, where each step represents an additional 10 percentage points.
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How deciles work
Deciles are used to simplify and summarize large datasets by grouping values into ten buckets. They are similar to percentiles (100 parts), quintiles (5 parts), and quartiles (4 parts). Analysts use deciles to identify extremes (e.g., top- and bottom-performing items) and to compare observations relative to a population.
Formula and calculation
A common method to locate the kth decile (Dk) in an ordered dataset of size n is to compute the position index:
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Index = (k × (n + 1)) / 10
If the index is an integer, Dk is the value at that position. If the index is fractional, interpolate between the two adjacent ordered values:
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Dk = value at floor(index) + fractional_part × (value at ceil(index) − value at floor(index))
Example (n = 30)
Using 30 ordered exam scores, compute:
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- D1 (k = 1): Index = (1 × 31) / 10 = 3.1 → between 3rd (55) and 4th (57) scores
- D1 = 55 + 0.1 × (57 − 55) = 55.2
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Interpretation: 10% of scores are below 55.2.
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D3 (k = 3): Index = (3 × 31) / 10 = 9.3 → between 9th (65) and 10th (66) scores
- D3 = 65 + 0.3 × (66 − 65) = 65.3
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Interpretation: 30% of scores are below 65.3.
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D5 (k = 5): Index = (5 × 31) / 10 = 15.5 → between 15th (76) and 16th (78) scores
- D5 = 76 + 0.5 × (78 − 76) = 77
- Interpretation: 50% of scores are below 77 (D5 equals the median).
Uses in finance and economics
- Performance ranking: Deciles compare mutual funds, portfolios, or securities, showing which are in the top or bottom 10% bands.
- Income distribution: Governments and researchers use deciles to measure inequality (e.g., share of total income held by the top decile).
- Risk and screening: Analysts can filter groups (e.g., lowest decile of valuations) for further investigation.
Key takeaways
- A decile divides data into 10 equal groups; each decile represents a 10% increment.
- Compute deciles by finding the position (k × (n + 1) / 10) and interpolating when necessary.
- Decile ranks are widely used to summarize distributions and compare relative performance or inequality.