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.
Song Lengths (seconds)
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
227 221 347 173 344 438 171 129 165 333
Arranged Data Set
129 165 171 173 221_(lower half)
227 333 344 347 438_(upper half)
The minimum and maximum values are 129 and 438, respectively.
The first quartile is 171 and the third quartile is 344. Since the number of values is even, the median is the average of the two middle values.
Median: 221+ 2272= 224
Box-and-Whisker Plot
We want to make a box-and-whisker plot using the obtained information.
Minimum:& 129
First Quartile:& 171
Median:& 224
Third Quartile:& 344
Maximum:& 438
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!
Song Lengths (seconds)
