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The lower quartile of a data set is the value such that a quarter of the observations are less than or equal to it, and three quarters are larger. The upper quartile is the value such that three quarters of the observations are less than or equal to it, and a quarter are larger.

Interquartile refers to between these two numbers.

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Q: What is the definition of the interquartile in math?
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Does there have to be an interquartile in math?

Yes, there does.


What is the meaing of interquartile range in math?

The interquartile range of a set of data is the difference between the upper quartile and lower quartile.


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Why do you multiply the interquartile range by 1.5 to find the outlier?

By definition a quarter of the observations are below the lower quartile and a quarter are above the upper quartile. In all, therefore, half the observations lie outside the interquartile range. Many of these will be more than the inter-quartile range (IQR) away from the median (or mean) and they cannot all be outliers. So you take a larger multiple (1.5 times) of the interquartile range as the boudary for outliers.