IQR

Description

IQR returns the (optionally corrected) interquartile range, a robust estimator of scale, using Excel’s “inclusive” QUARTILE.INC. The “corrected” IQR is scaled by dividing the raw IQR by the IQR of the standard normal distribution; thus for normally-distributed data it can be considered an estimate of the population standard deviation.

Syntax

IQR(data, [corrected=FALSE]) where

• data is the input univariate data (any shape), filtering out non-numeric values
• corrected is a boolean on whether to divide by the correction factor

The function returns a scalar value.

Example

Usage is straightforward: pass in the data as the first argument, and optionally choose to return the corrected value by passing TRUE as the second argument. Note that Excel interprets non-zero values as TRUE so it is common to see syntax like =IQR(data,1) in a cell formula.

Source Code

IQR = LAMBDA(
    data, // any shape
    [corrected], // apply correction (normalization)
    LET(
        correction, IF(ISOMITTED(corrected), FALSE, corrected),
        Q_1, QUARTILE.INC(data, 1),
        Q_3, QUARTILE.INC(data, 3),
        // correction 1.34897950039216 is the IQR of the std normal distr
        k, IF(correction, 1.34897950039216, 1),
        (Q_3 - Q_1) / k
    )
);