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.
Camera Prices
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
$280 $220 $224 $70 $410 $90 $30 $120
Arranged Data Set
$30 $70 $90 $120_(lower half)
$220 $224 $280 $410_(upper half)
The minimum and maximum values are $30 and $410, respectively. Since the number of values is even, the median is the average of the two middle values.
Median: $120+ $2202= $170
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: $70+ $902= $80
Analogously, the third quartile is the average of the two middle values in the upper half.
Q_3: $224+$2802=$252
The first quartile is $80 and the third quartile is $252.
Box-and-Whisker Plot
We want to make a box-and-whisker plot using the obtained information.
Minimum:& $30
First Quartile:& $80
Median:& $170
Third Quartile:& $252
Maximum:& $410
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!
Camera Prices (dollars)
