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.
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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!
Given Data Set
1 5 1 2.5 3 2 3.5 2 3 1.5 4 2 4 1 3 4.5
Arranged Data Set
1 1 1 1.5 2 2 2 2.5_(lower half)
3 3 3 3.5 4 4 4.5 5_(upper half)
The minimum and maximum values are 1 and 5, respectively.
Since the number of values is even, the median is the average of the two middle values.
Median: 2.5+ 32= 2.75
Moreover, because 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: 1.5+22=1.75
Analogously, the third quartile is the average of the two middle values in the upper half.
Q_3: 3.5+42=3.75
The first quartile is 1.75, the median is 2.75, and the third quartile is 3.75.
Box-and-Whisker Plot
We want to make a box-and-whisker plot using the obtained information.
Minimum:& 1
First Quartile:& 1.75
Median:& 2.75
Third Quartile:& 3.75
Maximum:& 5
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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