Quiz 1
The data below come from our class questionaire. Compare the
men's fastest driving speed to the women's.
One answer:
Men tend to list higher speeds than do women; the "typical" men's speed is
about 110mph while the typical women's speed is about 90 to 100 mph. The
men's speeds appear to be roughly uniformly distributed while the women's
seem to be unimodal (with the mode around 90 mph). The men's scores cover
a 100mhp range (from about 80 mph to 180 mph, more or less), while the women
-- excluding one potential outlier -- are more similar to one another: the
range is roughly 60 mph (from 60 to 120). On the other hand, one woman
drove 150 mhp, which puts her very high even with respect to the other men.
Notice that the comparison hits on all three components:
center, spread, shape. Also notice that it provides a fair amount of
detail.
Here's an example of a response from the class, although this, and
other responses, may be slightly ficitonalized to prove a point. Grade
it on a scale of 1-5 with 5 being the best.
"Men have a more even distribution for the faster speed
at which they drove their cats with a slight right skew. Women have
one typical value that seems to be at about 80. Overall, men appear
to have driven their cars faster."
Here's how I would grade. (1) Has s/he mentioned the center? Yes,
but only for the women. ("Women have one typical value..."). This isn't
compared to the typical value for the men. Also, it's a little unclear what
is meant by "one typical value". (2) Has s/he mentioned shape? Yes,
and s/he did a fairly good job. I would quibble, though, with the description
as an "even distribution" since we don't know what that means. If the
student had written "uniform" it would have been very clear. Another
drawback, though, is that the shape of the women's distribution isn't mentioned;
all we know is that it is less uniform than the men's and presumably not
skewed. (3) Did the student mention the spread? No. (4) Did the
student say anything that was just flat-out wrong? Well, we might quibble
over the "men appear to have driven their cars faster" because this is clearly
not true of all men. The word "appear" tends to soften this somewhat,
but overall it is not true. (5) What are the good points? This
person does a good job of describing things in the context of the data, and
I like the fact that he or she adds a conclusion at the end, even if I think
the conclusion was too strongly stated.
Overall, I would grade this somewhere between a 2 and a 3. Now
you try:
• "In general, men have driven faster than women. The peak of the male
values ia a little higher than the peak of the women's values."
What grade would you give and why? Compare
to my evaluation.
• "According to the histogram, women's speeds are distributed from about
60 mph to a few outlier in the hundreds. There are more women in comparison
to the men. The mens's speeds go from slowest of about 80 mhp to the
hundreds."
Compare your evaluation to mine.
If you'd like to try this some more, please go to the class
discussion forum. I've posted three more sample answers, and you
can discuss amongst yourselves which grades you'd give. Be harsh!