Arrange the data from least to greatest before identifying the minimum, maximum, and quartiles.
Minimum: 3.2 First Quartile: 4.2 Median: 5 Third Quartile: 6.15 Maximum: 12
Practice makes perfect
Quartiles are values that divide a data set into four equal parts. When quartiles are combined with the minimum and maximum values, it is often called the five-number summary of the data set.
The median, which can also be known as the second quartile (Q_2), separates the data into upper and lower halves.
The first quartile (Q_1) is the median of the lower half of the data.
The third quartile (Q_3) is the median of the upper half of the data.
Let's identify the five-number summary of the given data set. Do not forget to arrange the data from least to greatest first!
Given Data Set
4.5 3.2 6.3 5.2 5 4.8 6 3.9 12
Arranged Data Set
3.2 3.9 4.5 4.8_(lower half)
5
5.2 6 6.3 12_(upper half)
The minimum and maximum values are 3.2 and 12, respectively.
Since the number of values in each half is even, the first quartile is the average of the two middle values in the lower half.
Q_1: 3.9+4.52=4.2
Analogously, the third quartile is the average of the two middle values in the upper half.
Q_3: 6+6.32=6.15
The first quartile is 4.2 and the third quartile is 6.15. The median of the data is 5.
