Graphing Qualitative Variables
What type of graph is best for displaying proportions of small categories?
Pie chart.
What type of graph is most useful for displaying the shape of a distribution?
Histogram.
What is the primary characteristic we assess when looking at the shape of a distribution?
Whether it is symmetrical or skewed.
What could happen if a bar graph does not start at zero?
It can mislead viewers by exaggerating differences between categories.
When is it better to use a bar chart instead of a pie chart?
When there are a larger number of categories or comparing distributions.
Why would we use a histogram instead of a bar chart?
When we have a large number of observations in a distribution.
What is the name of a symmetrical distribution with a single peak?
Normal distribution (bell curve).
Why is it problematic if a pie chart contains too many categories?
It becomes cluttered and difficult to interpret.
What axis typically shows the number of observations in a bar chart?
Y-axis.
What is a box plot useful for?
Identifying outliers and comparing distributions.
What kind of distribution has multiple peaks?
Bimodal distribution.
What is a common mistake when labeling axes on a graph?
Not including units or clear category labels.
In a frequency table, what is the "frequency" and the "relative frequency"?
Frequency: the count/number of participants for each category.
Relative frequency: frequency of each category divided by total number of participants.
When is a line graph best used?
When we are looking at a change over periods of time.
Most students perform very well on an exam. What kind of distribution would we expect and why?
Negative skew because the tail is pointing to the left.
What is a misleading way to manipulate the scale of a graph?
Using unequal intervals on an axis to exaggerate trends.
What type of graph is best used if we want to compare many qualitative variables?
Name all the components of a box-and-whisker plot.
Box, median, 25th percentile, 75 percentile, upper and lower whiskers.
Bonus 100 points: outliers and mean.
Most people who fill out a stress survey report low levels of stress. What kind of distribution would we expect and why?
Positive skew, because the tail is pointing to the right.
Why should we avoid using 3D effects in bar charts?
They can distort perception and make it harder to compare values accurately; they add no additional information (unless you have 3 variables).