3 organizing and graphing quantitative data objective

Section 5.3: Organizing and Graphing
Quantitative Data
Objective: Organize quantitative data into frequency tables
An easy way to compile quantitative data would be to make a frequency or rela-
tive frequency table as we did with qualitative data.
Commute time to school
The data in the table below are the commute time to school (in minutes) for a
group of students attending a particular mathematics course. We would like to
create a frequency table.
10 15 17 20 25 20 3 30 17 15 5 15
60 8 25 15 25 22 38 10 14 30 30 18
Since there are no natural categories for this data we must create what are called
classes . Classes divide the number line into smaller pieces.
First let's ±nd the minimum commute time 3 minutes. Next ±nd the maximum
commute time 60 minutes. We can start our ±rst class at 3 minutes or back up a
few minutes. Let's start the ±rst class at 1 minute and use a class width of 10
minutes. The ±rst class is ²1 ³ 10.´ The 1 is considered the lower limit of the
class and the 10 is considered the upper limit of the class.
Next, we will determine the lower limits of the other classes. Add the class width
of 10 to our ±rst lower limit. This will give us 11. If we continue to add 10 the
remaining lower limits will be 21, 31, 41, and 51. The upper limits are deter-
mined by ±lling in the numbers that approach the next class' lower limit but do
not equal it. For example in the second row we chose 20 because it is the closest
whole number less than 21.
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The class width of 10 is evident by looking the diµerences in consecutive lower
class limits (This is also the case with consecutive upper class limits). They are
all 10. Once we made all the classes and made sure that the minimum and max-
imum can be placed in the table, we see that there are 6 classes. Now we must
determine how many commute times fall into each of the classes. There are sev-
eral strategies to tallying up the counts. You can mark them oµ as you go or pos-
sibly put unique symbols or marks next to the ones that are in the same classes.
This will help you avoid classifying a value twice or forgetting a data value alto-
gether. Once all the symbols are there you can count them.
Vocabulary:
Classes = range of data values used to group the data.
Lower class limit = the smallest value that goes in a class.
Upper class limit = the largest value that goes in a class.
Class width = the diµerence between two consecutive lower class limits.
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Objective: Create a histogram for quantitative data
We can take our frequency table and create a graph of the information. This
graph is called a histogram. A histogram is like a bar graph. The classes are
along the horizontal axis and the frequencies are demonstrated with the vertical
axis. The bars need to touch in a histogram because we want to imply that the
classes are adjacent and represent a continuum on the number line.