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The Decile Calculator divides a dataset into ten equal parts using nine cut-off points called deciles. While quartiles split data into four groups and percentiles into one hundred groups, deciles provide a middle ground that is useful for ranking analysis, income distribution studies, academic grading, and performance benchmarking.
Each decile represents 10% of the data distribution. D1 (the first decile) marks the value below which 10% of observations fall, D5 is the median (50%), and D9 marks the top 10% threshold. Deciles are especially prominent in economics for analyzing wealth distribution, in finance for portfolio performance ranking, and in education for class standing reports. This calculator supports up to 10 data values and computes any decile from D1 through D9 using linear interpolation.
Deciles are special cases of percentiles. The kth decile \(D_k\) corresponds to the \((10k)\)th percentile. To compute:
$$D_k = P_{10k}$$
The calculation follows the same linear interpolation method as percentiles:
$$L = \frac{10k}{100} \times (n + 1) = \frac{k(n+1)}{10}$$
If \(L\) is an integer, \(D_k\) is the value at position \(L\) in the sorted dataset. Otherwise, interpolate:
$$D_k = x_{\lfloor L \rfloor} + (L - \lfloor L \rfloor)(x_{\lceil L \rceil} - x_{\lfloor L \rfloor})$$
The nine deciles \(D_1\) through \(D_9\) create ten bins, each containing approximately 10% of the data. Note that \(D_5\) equals the median, \(D_1\) corresponds to Q1 (approximately, since Q1 = P25 = D2.5), and \(D_5\) = Q2 = median exactly.
Each decile boundary tells you the threshold for a specific 10% segment of your data. If the 7th decile (D7) for exam scores is 82, then 70% of students scored at or below 82. The interdecile range (D9 - D1) captures the spread of the central 80% of data, offering a robust alternative to the full range that is less sensitive to outliers.
In economic analysis, the ratio D9/D1 is used as an inequality measure — a larger ratio indicates greater income disparity within a population.
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For 10 values, D5 is at rank position 5.5. Interpolating between 70 (5th) and 75 (6th): 70 + 0.5*(75-70) = 72.5. This is the median.
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With 8 income values, D9 falls at rank 8.1 near the maximum value. 90% of earners make at or below this level.
Quartiles divide data into 4 equal parts (25% each), while deciles divide into 10 equal parts (10% each). Deciles provide finer granularity. Q1 corresponds to D2.5, Q2 (median) = D5, and Q3 corresponds to D7.5.
Economists rank households by income and divide them into decile groups. The D9/D1 ratio measures inequality. A ratio of 10 means the top 10% earn at least 10 times the bottom 10% threshold.
Yes. The 5th decile (D5) corresponds to the 50th percentile, which is the median by definition.
Ideally at least 20-30 values, so each decile group contains 2-3 data points. With fewer values, deciles are rough estimates obtained through interpolation.
The interdecile range is D9 - D1, representing the spread of the central 80% of data. It is more robust than the full range because it excludes the extreme 10% on each end.
This calculator computes one decile at a time. To find all nine, simply change the target decile from 1 through 9 and record each result.
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