Find the Interquartile Range (H-Spread) 48 , 52 , 56 , 64 , 61 , 20 , 48 , 51 , 58 , 48 , 78

There are ${\displaystyle 11}$ 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.

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 ${\displaystyle 48}$ and the third quartile ${\displaystyle 61}$. In this case, the difference between the first quartile ${\displaystyle 48}$ and the third quartile ${\displaystyle 61}$ is ${\displaystyle 61-\left(48\right)}$.