Find the Interquartile Range (H-Spread) 800 , 756 , 810 , 836 , 731 , 542 , 589

There are ${\displaystyle 7}$ observations, so the median is the middle number of the arranged set of data. Splitting the observations either side of the median gives two groups of observations. The median of the lower half of data is the lower or first quartile. The median of the upper half of data is the upper or third quartile.

Arrange the terms in ascending order.

The median is the middle term in the arranged data set.

The lower half of data is the set below the median.

The median is the middle term in the arranged data set.

The upper half of data is the set above the median.

The median is the middle term in the arranged data set.

The interquartile range is the difference between the first quartile ${\displaystyle 589}$ and the third quartile ${\displaystyle 810}$. In this case, the difference between the first quartile ${\displaystyle 589}$ and the third quartile ${\displaystyle 810}$ is ${\displaystyle 810-\left(589\right)}$.