Rewrite the values in the proper number of copies each, arranging them from least to greatest. Identify the minimum, maximum, and quartiles. You will need these values to make the box-and-whisker plot.
Studying Time (hours)
Practice makes perfect
We are given a dot plot representing the numbers of hours students spent studying for an exam.
Let's start with writing down the set of numbers including a copy of each number for each dot assigned to it in the plot and arranging it from the least to greatest.
Given Data Set
0 0 1 1 1 1 2 2 2 2 2 2 3 3 3 4 4 5 5 7
To make a box-and-whisker plot, we need to identify the minimum, first quartile, median, third quartile, and maximum of the given data set. 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
0 0 1 1 1 1 2 2 2 2_(lower half)
|
2 2 3 3 3 4 4 5 5 7_(upper half)
The minimum and maximum values are 0 and 7, respectively.
Since the number of values is even, the median is the average of the two middle values.
Median: 2+ 22= 2
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: 1+ 12= 1
Analogously, the third quartile is the average of the two middle values in the upper half.
Q_3: 3+42=3.5
The first quartile is 1 and the third quartile is 3.5.
Box-and-Whisker Plot
We want to make a box-and-whisker plot using the obtained information.
Minimum:& 0
First Quartile:& 1
Median:& 2
Third Quartile:& 3.5
Maximum:& 7
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!
Studying Time (hours)
