[FEATURE] interquartile range (IQR)

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To calculate the average of a dataset while removing big outliers, the interquartile range (IQR) method can be used.

The IQR serves as a robust measure of variability because it is less sensitive to outliers compared to the range.

Resources: https://www.youtube.com/watch?v=qLYYHWYr8xI&t=106s

• A small IQR (like 3) indicates that the middle 50% of the data is relatively close together, showing lower variability in the core values.
• A larger IQR would indicate that the data is more spread out, suggesting greater variability within the central 50%.
• The IQR can be used to compare variability between different datasets. For example, if another dataset has an IQR of 8, its middle 50% is more spread out than yours.

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Sample values

From: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/cc-6th/v/calculating-interquartile-range-iqr

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Input: [4, 4, 6, 7, 10, 11, 12, 14, 15]

median = 10
iqr = 13-5 = 8

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Input: [7, 9, 9, 10, 10, 10, 11, 12, 12, 14]

median = [10,10]
iqr = 12-9 = 3

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Input: [7, 7, 31, 31, 47, 75, 87, 115, 116, 119, 119, 155, 177];

Median: 87

Q1=31 (median of lower half, from row 1 to 6, (31+31/2))
Q3=119 (median of upper half, from row 8 to 13, ((119+119/2))

IQR = Q3 − Q1 = 119 - 31 = 88

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More here: https://en.wikipedia.org/wiki/Interquartile_range

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Other Recommendations

• For mild outliers, use the trimmed mean or Winsorized mean
• For highly skewed datasets with severe outliers, the median is the most robust choice
• If the data has positive values and spans orders of magnitude, the geometric mean is ideal