A quantitative variable is a variable that takes
on numerical values for which arithmetic makes sense.
A categorical or qualitative variable is a variable
that records which category a person place or thing falls into.
Questions about data
What variables are being measured?
Are these variables appropriate for answering the
question(s) of interest?
What are the units of measurement?
How are the data recorded?
Graphical Displays
Why are graphing techniques useful?
Examine the overall shape of a distribution - (symmetric
or skewed?)
Look for deviations from the overall shape - (unusual
observations, gaps, etc.)
Locate the center of the distribution
Stem and Leaf Plots
Separate each observation into a stem and a leaf.
List the stems vertically in increasing order from
top to bottom.
Add the leaves (typically the last digit) to the
right of the stems.
Histograms
Divide the range of the data into classes of equal
width.
Count the number of observations in each class.
Compute the relative frequency or percent for each
class.
Erect bars over each class interval.
Graphical Displays with Minitab (Open p:\data\math\stats\Day1 F2009.mtw)
Bar Charts (Graph > Bar Chart)
Pie Charts (Graph > Pie Chart)
Dotplots (Graph > Dotplot)
Stemplots (Graph > Stem-and-Leaf)
Histograms (Graph > Histogram)
Time Plots (Graph > Scatterplot OR Graph > Time Series
Plot)
Exercise 3.51 on page 133
In Class Exercises
Construct appropriate graphs to visually summarize the information collected on the data cards for the following variables: sex, distance, height, handedness, coins, whitestring, blackstring, reading, TV, pulse, and texting.
I was very surprised by the amount of reading you expect to be doing this semester. Construct an appropriate graph and describe the shape of this distribution. Estimate the center of the distribution from your graph.
Is the shape of the distribution for guesses of the length of the black string the same as the distribution of guesses for the length of the white string?
The actual length of the white sting is 46". Is the overall distribution of guesses centered at this value?
The actual length of the black string is 48". Is the overall distribution of guesses centered at the appropriate value?
Use appropriate graphical displays and descriptive statistics to make appropriate comparisons between men and women for different variables in the data set we collected during the first class.
Use appropriate graphical displays and descriptive statistics to make appropriate comparisons between the two sections for different variables in the data set we collected during the first class.
Caution is necessary when constructing histograms
from frequency distributions given in magazines, newspapers, journal articles,
etc. The authors of "Self-Reports of Academic Performance," an article
which appeared in Soc. Methods and Research (1981), studied the difference
in GPA, reported - actual, for each of the students in a sample. Specify
the height of each bar in a correct histogram for the frequency distribution
below and sketch the histogram.