Graphical Methods Comparing Hours Spent at School and at Work
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Statistical Topic:
Data can be described both numerically and graphically. This
type of statistics is called descriptive statistics because it describes
sample data. We can start to recognize data characteristics such
as center and spread by first displaying the observations into some type
of graphical form. Two statistical graphs which help students represent
data in such form are the stem-and-leaf display and the histogram. |
Student Issue:
All students value education for many reasons but getting a good job
in an area of interest to them is certainly one of the most important.
A set of variables will be collected from each student comparing the type
of job each student currently has compared to the type of job each would
like to have in the future. One of the most important factors in
getting the job we really want is education. We all have spent and
are still spending a lot of time at school. This data set will compare
the number of hours spent at school to the number of hours per week spent
working. The two variables in this data set used for graphical displays
are hours per week and the place, school or work, where the hours were
spent. |
Data Set:
Collect data from each student and place on one piece of paper or fill
out the following table: Table 1. Class
Data For Job and School Variables. |
Goal of this Data Analysis Lab:
Using the results of this class data collection, students will learn
how to draw a back-to-back stem-and-leaf display. Students will also learn
how to draw two comparative histograms and interpret these graphical displays. |
Statistical Techniques:
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Each student will fill in his/her personal information for the job and
school variables. For every variable in this data set determine if
each variable is quantitative-continuous, quantitative-discrete, categorical-ordinal
or categorical-nominal.
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Create a research question appropriate for comparing the hours worked per
week for both school and work. This research question must contain
both the numerical variable measured and the categorical variable, which
divides the data set into the two samples.
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Draw a back-to-back stem-and-leaf display comparing average hours per week
spent at school with the average hours worked per week. Make sure to title
this plot and label appropriately.
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For the two samples, create a frequency distribution table that divides
the data set into equal class intervals and counts the number of observations
for each class for both times spent at school and at work. Next to the
frequency for each class interval covert to a percent of the total number
of observations in the sample (or a fraction). This is called relative
frequency.
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Create two frequency histograms with the same scale (same classes on the
x-axis and same y-axis) for average hours per week spent at school and
at work. Make sure to title each plot and label appropriately. Write
a descriptive paragraph interpreting these two histograms focusing on comparing
the middle, spread, shape and evidence of outliers. Is the shape of these
graphs affected by using relative frequencies for the y-axis compared to
using frequencies? If you are unsure of the answer, then draw one of the
histograms using the relative frequency on the y-axis instead of the frequency.
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How does the shape of your stem-and-leaf compare with your two histograms?
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| Social Commentary: |
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How do the jobs students have now compare with jobs students would like
to have in the future?
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What factors other than education influence whether you get a job you really
want?
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