Arrange the data from least to greatest before identifying the minimum, maximum and quartiles. You will need these values to make the box-and-whisker plot.
Cat Lengths (in inches)
Practice makes perfect
We want to identify the minimum, first quartile, median, third quartile, and maximum of the given data set. Then we will make a box-and-whisker plot using these values. Let's do these things one at a time.
Values
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
16 18 20 25 17 22 23 21
Arranged Data Set
16 17 18 20_(lower half)
|
21 22 23 25_(upper half)
The minimum and maximum values are 16 and 25, respectively.
Since the number of values is even, the median is the average of the two middle values.
Median: 20+ 212= 20.5
Moreover, the number of values in each half is even, therefore the first quartile is the average of the two middle values in the lower half.
Q_1: 17+ 182= 17.5
Analogously, the third quartile is the average of the two middle values in the upper half.
Q_3: 22+232=22.5
The first quartile is 17.5 and the third quartile is 22.5.
Box-and-Whisker Plot
We want to make a box-and-whisker plot using the obtained information.
Minimum:& 16
First Quartile:& 17.5
Median:& 20.5
Third Quartile:& 22.5
Maximum:& 25
This type of graph summarizes a set of data by displaying it along a number line. It consists of three parts: a box and two whiskers.
The left whisker extends from the minimum to the first quartile.
The box extends from the first to the third quartile and has a vertical line through the median.
The right whisker extends from the third quartile to the maximum.
Let's make our box-and-whisker plot!
Cat Lengths (in inches)
