Performance Overview
The First Hourly
Spring 2008
Score Distribution
There were 94 tests taken.
The mean score among the 94
tests was approximately 75.8%.
The lowest scores among the 94
tests was 0%.
Approximately 95% of the
scores were at 21% or more.
Approximately 90% of the
scores were at 40% or more.
Approximately 75% of the
scores were at 68% or more.
Approximately 70% of the
scores were at 72% or more.
Approximately 60% of the
scores were at 76% or more.
Approximately 50% of the
scores were at 83% or more.
Approximately 40% of the
scores were at 88% or more.
Approximately 30% of the
scores were at 92% or more.
Approximately 25% of the
scores were at 94% or more.
Approximately 20% of the
scores were at 96% or more.
Approximately 10% of the
scores were at 97% or more.
Approximately 5% of the scores were at 98% or more.
The highest scores among the
94 tests were at 100%.
Tabular Summaries
|
HR1 |
Frequency |
Percent |
|
[0,40) |
9 |
9.57 |
|
[40,50) |
4 |
4.26 |
|
[50,60) |
4 |
4.26 |
|
[60,70) |
10 |
10.64 |
|
[70,80) |
16 |
17.02 |
|
[80,90) |
17 |
18.09 |
|
[90,100) |
32 |
34.04 |
|
100 |
2 |
2.13 |
|
HR1 |
Frequency |
Percent |
|
[0,50) |
13 |
13.83 |
|
[50,60) |
4 |
4.26 |
|
[60,70) |
10 |
10.64 |
|
[70,80) |
16 |
17.02 |
|
[80,90) |
17 |
18.09 |
|
[90,100) |
32 |
34.04 |
|
100 |
2 |
2.13 |
|
HR1 |
Frequency |
Percent |
|
[0,60) |
17 |
18.09 |
|
[60,70) |
10 |
10.64 |
|
[70,80) |
16 |
17.02 |
|
[80,90) |
17 |
18.09 |
|
[90,100) |
32 |
34.04 |
|
100 |
2 |
2.13 |
|
HR1 |
Frequency |
Percent |
|
[0,60) |
17 |
18.09 |
|
[60,70) |
10 |
10.64 |
|
[70,80) |
16 |
17.02 |
|
[80,90) |
17 |
18.09 |
|
[90,100] |
34 |
36.17 |
|
HR1 |
Frequency |
Percent |
|
[0,70) |
27 |
28.72 |
|
[70,90) |
33 |
35.11 |
|
[90,100] |
34 |
36.17 |
Detail
I
checked for full detail in your work, and docked points for deficient detail.
The process is the point, the correct answer(s) naturally flow from the correct
process.
Algebra and Arithmetic
Clean up your work, and watch
the details. Clean up the arithmetic: (1/4)*(1/2) is not 1/6; (1/8)+(1/8)
is not 1/16. If your algebra and arithmetic are deficient, get the required
remediation.
Formatting
Space out your work and use
one side only of the provided work sheets. I have provided extensive examples
of acceptable and preferred formatting.
Interpretation and
Discussion
This was a clear problem for
some students I view this as a matter of work ethic and attention to detail.
Writing is a regular part of test work, and continued neglect will draw
additional loss of points. Study the test banks, pay attention to case
summaries, and provide the required writing.
Case Type Comments
Long Run Argument / Perfect Samples
We
begin with a model, typically specified as a list of events (F) and their corresponding
probabilities (Pr{F}=PF). The Long Run Argument is a way of
describing the meaning of the model probabilities. The Long Run Argument
indicates hoe the probabilities PF predict the prevalence of the events F in long runs of sampling each long run is an indefinitely large hypothetical
random sample, that is, a very large random sample of unstated size.
Next,
a sample size (n) is provided, and a perfect sample is constructed one count per
event is computed as EF
= n*Pr{F} = n*PF. The
likely behavior of random samples of size n is predicted by the perfect sample
of the same size.
Dice / Random Variables
We
list the 12
triplets by fixing the 1st die and then working with the other two
dice. Fix D1 at 1, then: (1,2,3), (1,2,4), (1,3,3) and (1,3,4). Fix D1 at 2,
then: (2,2,3), (2,2,4), (2,3,3) and (2,3,4). Fix D1 at 4, then (4,2,3),
(4,2,4), (4,3,3) and (4,3,4). Then, for example, Pr{(2,3,4)} = Pr{2 from
D1}*Pr{3 from D2}*Pr{4 from D3} = (1/3)*(1/2)*(1/2) = 1/12.
Show
details for each triplet.
Conditional Probability by Formula
The
definition of conditional probability is based on the formula Pr{A|B} =
Pr{A and B}/Pr{B}. A number of students did not understand the definition of conditional
probability and used variants like Pr{A|B} = Pr{A}/Pr{B}. Other students computed Pr{A and B} and Pr{B}, but did not compute Pr{A|B}.
Probability Computation Rules
Probabilities
P are between 0 and 1: 0 £ P £ 1 - a number of students presented probabilities outside this range.
Additionally, a number of students did not demonstrate the Complementary
Rule as
indicated.
Further Comments
Follow the protocol: show your work and details, write on one side of the sheets.
Attention to detail: Clean up your work, and watch the details. Clean up the arithmetic:
(1/4)*(1/2) is not 1/6; (1/8)+(1/8) is not 1/16.
Major issues include:
Deficient knowledge of the
definition of conditional probability;
Deficient knowledge of the
definitions for the long run argument and for perfect samples;
Deficient knowledge of the
computation of random variables;
Insufficient familiarity with
the material in general.
If your first score is low: Remember the grading policy if you dont, look it up.
The worst of the three test scores drop.
Remediation: the
standard for performance is my keys and not your neighbors tests. Do not
shop for points with me. If your points do not add up, let me know. Compare
your test work to my key note where and why you lost points. Note the cases
in which you lost the most points. Think of a revised tool-sheet, one that would
prevent these problems form re-occurring. Write that tool-sheet.
Self Audit, Patterns of
Point Loss, Revision of Analytic Narratives
Find patterns in your losses
why did you lose points? Did you lose most points in a case or two, or were
your losses spread out over all of the cases? Did you lose points over algebra?
Detail? List your cases in order of point loss, from most to fewest. For each
case with point loss, determine the reasons for the losses. Check your analytic
narratives and modify them to avoid these losses.