The IQM is a *truncated mean* and so is very similar to the scoring method used in sports that are evaluated by a panel of judges: *discard the
lowest and the highest scores; calculate the mean value of the remaining
scores*.

In calculation of the IQM, the lowest 25% and the highest 25% of the
scores are discarded. These points are called the first and third
quartiles, hence the name of the IQM. (Note that the
*second* quartile is also called the median). The method is best
explained with an example:

Consider the following dataset:

- 5, 8, 4, 38, 8, 6, 9, 7, 7, 3, 1, 6

- 1, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9, 38

~~1, 3, 4~~, 5, 6, 6, 7, 7, 8,~~8, 9, 38~~

- x
_{IQM}= (5 + 6 + 6 + 7 + 7 + 8) / 6 = 6.5

- Like the median, the IQM insensitive to outliers; in the example given, the highest value (38) was an obvious outlier of the dataset, but its value is not used in the calculation of the IQM. On the other hand, the common average (the arithmetic mean) is sensitive to these outliers: x
_{mean}= 8.5. - Like the mean, the IQM is a discrete parameter, based on a large number of observations from the dataset. The median is always equal to
*one*of the observations in the dataset (assuming an odd number of observations). The mean can be equal to*any*value between the lowest and highest observation, depending on the value of*all*the other observations. The IQM can be equal to*any*value between the first and third quartiles, depending on*all*the observations in the interquartile range.

- 1, 2, 3, 4, 5

We can solve this by using a weighted average of the quartiles and the interquartile dataset:

Consider the following dataset of 9 observations:

- 1, 3, 5, 7, 9, 11, 13, 15, 17

~~1, 3~~, (5), 7, 9, 11, (13),~~15, 17~~

The IQM is now calculated as follows:

- x
_{IQM}= {(7 + 9 + 11) + 0.75 x (5 + 13)} / 4.5 = 9