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What exactly is the IQR and what does it stand for?

The median is a number that splits the data into two equal halves and is one of the measures of central tendency in statistics. The data in the 50% range is below the median value while the data in the 50% range is above the median value.

The partition values that divide the data into four equal halves are called quartiles. The first quartile is the value below which 25% of the data is found and above which 75% of the data is found. The median is represented by the second quartile. The third quartile is the value below which 75% of the data is found, and beyond which 25% of the data is found.

The difference between the third and first quartiles is known as the interquartile range. When arranged from lowest to highest, it describes the median 50% of values.

IQR is calculated using the following formula:

$IQR=Q_3-Q_1$

In the given example, we are given the below parameters about the population:

$$\begin{gathered} \mathrm{μ}=1000\mathrm{FTES} \\ median=1014FTES \\ \mathrm{σ}=474FTES \\ firstquartile=528.5\mathrm{FTES} \\ thirdquartile=1447.5FTES \\ n=29years \end{gathered}$$

Where 528.5 represents the first quartile and 1447.5 represents the third quartile, the IQR is as follows:

$IQR=1447.5-528.5=919\mathrm{FTES}$

Hence IQR=919, which represents the middle 50% of FTES.