Quartile Deviation (Semi-Interquartile Range)

The range depends only on the two extremes. The Quartile Deviation improves on this by using the quartiles, which describe the middle of the data and ignore the outer tails. Recall that the first quartile $Q_1$ cuts off the lowest $25\%$ of the data and the third quartile $Q_3$ cuts off the lowest $75\%$; the middle $50\%$ of the values lie between $Q_1$ and $Q_3$.

Finding the quartiles. For raw (ungrouped) data, arrange the values in ascending order and locate the positions

interpolating between neighbouring values when the position is not a whole number. For a grouped frequency distribution the quartiles are read from the cumulative frequencies using the interpolation formula $Q_1 = L + \dfrac{\frac{N}{4} - \text{c.f.}}{f}\times h$ (and $\frac{3N}{4}$ for $Q_3$), exactly as studied for partition values.