Find the Interquartile Range (H-Spread) 14 , 24 , 35 , 37 , 43 , 35 , 45 , 24 , 29 , 41 , 45 , 37 , 19 , 45 , 52

There are ${\displaystyle 15}$ 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 ${\displaystyle 24}$ and the third quartile ${\displaystyle 45}$. In this case, the difference between the first quartile ${\displaystyle 24}$ and the third quartile ${\displaystyle 45}$ is ${\displaystyle 45-\left(24\right)}$.