Partition Values are statistical measures that divide a dataset into specific parts, helping in understanding the distribution of data. These include quartiles, deciles, and percentiles.
Quartiles:
Quartiles divide the dataset into four equal parts, each containing 25% of the data points.
Key Quartiles:
- Q1 (First Quartile): The value below which 25% of the data lies.
- Q2 (Second Quartile/Median): The value below which 50% of the data lies.
- Q3 (Third Quartile): The value below which 75% of the data lies.
Formula:
Qk = k(n+1) / 4
Where
k is the quartile position (1, 2, or 3)
n is the number of observations.
Deciles:
Deciles divide the dataset into ten equal parts, each containing 10% of the data points.
Key Deciles:
- D1 (First Decile): The value below which 10% of the data lies.
- D5 (Fifth Decile): The value below which 50% of the data lies (this is also the median).
- D9 (Ninth Decile): The value below which 90% of the data lies.
Formula:
Dk = k(n+1)10
Where k is the decile position (1 to 9).
Percentiles:
Percentiles divide the dataset into 100 equal parts, each containing 1% of the data points.
Key Percentiles:
- P1 (First Percentile): The value below which 1% of the data lies.
- P50 (Fiftieth Percentile): The value below which 50% of the data lies (this is also the median).
- P99 (Ninety-ninth Percentile): The value below which 99% of the data lies.
Formula:
Pk = k(n+1) / 100
Where k is the percentile position (1 to 99).
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