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.
Minimum: 25 First Quartile: 30.5 Median: 90 Third Quartile: 102.5 Maximum: 112 Example Box-and-Whisker Plot:
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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!
The minimum and maximum values are 25 and 112, respectively. The median of the data is 90. Since the number of values in the lower half is even, the first quartile is the average of the two middle values in this half.
First Quartile: 29+ 322= 30.5
Similarly, since the number of values in the upper half is even, the third quartile is the average of the two middle values in this half.
Third Quartile: 97+ 1082= 102.5
Box-and-Whisker Plot
We want to make a box-and-whisker plot using the obtained information.
Minimum:& 25
First Quartile:& 30.5
Median:& 90
Third Quartile:& 102.5
Maximum:& 112
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!
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