Arrange the data from least to greatest before identifying the minimum and maximum values and quartiles.
You will need these values to make the box-and-whisker plot.
Example Box-and-Whisker Plot:
Masses of lions (Kg)
Distribution: Skewed left
Practice makes perfect
We want to make a box-and-whisker plot that represents the data set. In order to do that, we will first identify the minimum, first quartile, median, third quartile, and maximum of the given data. 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!
The minimum and maximum values are 120 and 230, respectively.
Since the number of values in the lower half is even, the first quartile is the average of the two middle values.
First quartile: 160+ 1802= 170
The number of values in the upper half is also even, therefore the second quartile is the average of the two middle values.
Second quartile: 210+ 2302= 220
The total number of values is also even, therefore the median is the average of the two middle values.
Median: 200+ 2002= 200
Box-and-Whisker Plot
We want to make a box-and-whisker plot using the obtained information.
Minimum:& 120
First Quartile:& 170
Median:& 200
Third Quartile:& 220
Maximum:& 230
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!
Masses of lions (Kg)
Distribution
Now, let's find the distribution of the data. We can see that most of the data is on the right side of the plot and that the left whisker is longer than the right one. Therefore, the distribution is skewed left.
