5 Number Summary

In Quarter & Spread, we looked at quartiles and found that when we quarter a data set, we can determine 5 key values. These are the minimum value, the lower quartile, the median, the upper quartile and the maximum value. So here is the 5 number summary:

 

Minimum value

The minimum value is the lowest score in a data set.

 

Lower quartile

The lower quartile is also called the first quartile. It is the middle score between the lowest score and the median and it represents the $25$25th percentile.

The lower quartile is the $\frac{n+1}{4}$n+14​th score, where $n$n is the total number of scores.

 

Median

The median is the middle score in a data set.

It is calculated as the $\frac{n+1}{2}$n+12​th score, where $n$n is the total number of scores.

 

Upper quartile

The upper quartile is also called the third quartile. It is the middle score between the highest score and the median and it represents the $75$75th percentile.

The upper quartile is the $\frac{3\left(n+1\right)}{4}$3(n+1)4​th score, where $n$n is the total number of scores.

 

Maximum value

The maximum value is the highest score in a data set.

 

What it all means

The five numbers from the five number summary break up our set of scores into four parts. Have a look at the diagram here:

So knowing the five numbers can help us identify key regions of $25%$25%, $50%$50%, and $75%$75% of the scores.

It also leads nicely to the development of box plots that we will learn about soon.

 

Practice questions

Question 1`

Question 2