The interquartile range (IQR) describes the population subset encompassing the middle 50% of a normal distribution.
The IQR spans the second and third quartiles, with the two quartiles separated by the median value.
The IQR corresponds to the normal distribution curve from –0.6745 SD below to +0.6745 SD above the median.
standard deviation =
= IQR / 1.349
The first quartile starts at –2.698 SD below the mean and and runs to –0.6745 SD below the mean. The value of the lower delimiter:
lower delimiter for first quartile =
= (lower delimiter for IQR) – (1.5 * (IQR))
= (median) – (2 * (IQR))
The fourth quartile starts at +0.6745 SD above the mean and runs to +2.698 SD above the mean. The value of the upper delimiter:
upper delimiter for fourth quartile =
= (upper delimiter for IQR) + (1.5 * (IQR))
= (median) + (2 * (IQR))
