Arrange the data from least to greatest before identifying the minimum, maximum, and quartiles.
Minimum: 49 First Quartile: 50.5 Median: 52 Third Quartile: 54 Maximum: 67
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
55 53 67 52 50 49 51 52 52
Arranged Data Set
49 50 51 52_(lower half)
52
52 53 55 67_(upper half)
The minimum and maximum values are 49 and 67, 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: 50+512=50.5
Analogously, the third quartile is the average of the two middle values in the upper half.
Q_3: 53+552=54
The first quartile is 50.5 and the third quartile is 54. The median of the data is 52.
