In the field of assessing exams, different methods are used
to measure how well individuals perform. DoExam currently uses two scoring
systems: Normal Scoring and Normal Distribution. While Normal Scoring is a
familiar and straightforward method, Normal Distribution adopts a different
application and approach, focusing on the overall performance distribution. In
this article, we will explore how both systems work using a hypothetical math
exam. Our goal is to explain their differences, benefits, and uses in
evaluating student performance.
Normal Scoring System
As the name suggests, the Normal Scoring System is a
straightforward and widely used method for calculating exam scores. Imagine you
are taking a math exam with three sections: Algebra, Geometry, and Calculus,
each worth 100 points. Let us see how Normal Scoring works in action:
Individual Section Scores
You score 80 points in
Algebra, 90 points in Geometry, and 70 points in Calculus. Each individual
section score is converted into a percentage by dividing the points earned by
the total possible points and multiplying by 100. So, you scored 80% in Algebra,
90% in Geometry, and 70% in Calculus.
Overall Exam Result
But what about your overall
score? Normal Scoring calculates this by taking the average (mean) of the
individual section scores, considering their respective weights. Let us say
Algebra carries 3 weight, Geometry 4, and Calculus 3. Your overall score would
be:
Overall Result = (3 * 80) + (4 * 90) + (3 * 70)/10 = 240 +
360 + 210/10 = 81
As you can see, Normal Scoring offers a transparent and
clear-cut way to determine your performance on each section and the overall
exam.
Normal Distribution System
While the Normal Scoring System provides a transparent
approach, the Normal Distribution Scoring System takes a more statistical
route, considering the overall performance of all exam-takers. Let us revisit
our math exam example to grasp this method:
Individual Section Scores
Imagine you scored 80 points in Algebra on an exam where the
mean score was 75 points and the standard deviation was 10 points in each
section. Compared to the Normal Scoring system, where everyone gets the same
points for 80, the Normal Distribution method accounts for your score's
position relative to others. Since your score is one standard deviation above
the mean in Algebra, you might receive additional points depending on the
specific distribution used.
Understanding Standard Deviation: Imagine the scores
of all exam-takers in a given section forming a bell-shaped curve, with the
mean score at the peak. The standard deviation represents the spread of scores
around the mean. A lower standard deviation indicates scores clustered closer
to the mean, while a higher one shows more variation. Overall Exam Result
Similar to the Normal Scoring
System, your overall score is calculated using a weighted average. However, the
individual section scores obtained through the Normal Distribution method
(considering your position within the overall distribution) are used instead of
raw scores.
Key Differences
While both systems calculate weighted averages, they differ
in how they treat individual scores:
- Normal Scoring: Awards the same points for a specific
score regardless of the overall distribution amongst participant.
- Normal Distribution Scoring: Considers your score's
position relative to the entire exam (or a specific group), potentially
awarding more points for scores above the mean and vice versa.
Benefits of Normal Distribution Scoring
- Provides a more discerning understanding of individual
performance by considering relative standing within the exam participants.
- Can be used to adjust for variations in difficulty between
different exam versions or sections.