Weighted Total
Grade Calculation Equations
Blackboard Learn
Grade Center
17 September 2014
Weighted Total Grade Calculations in
the Blackboard Learn Grade Center
1
Total Score Calculations in General
• Total Possible Score
= PossibleScore1 + PossibleScore2 +...
• Total Given Score
= GivenScore1 + GivenScore2 +...
• Given Fraction of the Total Possible Scores
= Total Given Score / Total Possible Score (≤ 1)
• Given Percentage of the Total Possible Scores
= 100 x Given Fraction of the Total Possible Scores
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
2
Total Score Calculations in General
Given Percentage of the Total Possible Scores
= 100 x [(GivenScore1 + GivenScore2 + ...) /
(PossibleScore1 + PossibleScore2 + ...)]
= 100 x (Total Given Score / Total Possible Score)
Ratio of Total Given Scores to Total Possible Scores
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
3
Weighted Score Calculations in General
Total Weighted Possible Score
= [ Weight1 x PossibleScore1 + Weight2 x PossibleScore2 + ... ]
/( Weight1 + Weight2 + … )
Total Weighted Given Score
= [ Weight1 x GivenScore1 + Weight2 x GivenScore2 + ... ]
/( Weight1 + Weight2 + … )
Given Fraction of the Weighted Possible Scores
= Total Weighted Given Score / Total Weighted Possible Score (≤ 1)
Given Percentage of the Weighted Possible Scores
Weighted
Calculations
in
= 100 x Given Fraction
of Total
theGrade
Possible
Weighted
Scores
17 September 2014
Blackboard Learn
4
Some Shorthand for Score Calculations
•
•
•
•
•
GivenScore1 = GS1
GivenScore2 = GS2
PossibleScore1 = PS1
PossibleScore2 = PS2
Given Score Scaled by its Possible Score
= GS1/PS1 (≤ 1)
• …
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
5
Weighted Score Calculations in General
Total Weighted Possible Score
= ( W1 x PS1 + W2 x PS2 + ... ) / (W1 + W2 + …)
= The Whole (The Maximum Possible)
Total Weighted Given Score
= ( W1 x GS1 + W2 x GS2 + ... ) / (W1 + W2 + …)
= The Part Given
Given Fraction of the Weighted Possible Scores
= The Part Given / The Whole
= (W1 x GS1 + W2 x GS2 + ...)
/ (W1 x PS1 + W2 x PS2 + ...) (≤ 1)
Given Percentage = 100 x Given Fraction …
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
6
Given Percentage of the Weighted
Possible Score Calculations in BbLearn
“Given Fraction of the Weighted Possible Score“ in BbLearn
= [ Weight1 x ( GivenScore1 / PossibleScore1 ) +
Weight2 x ( GivenScore2 / PossibleScore2 ) + ... ]
/( Weight1 + Weight2 + … )
= [ W1 x (GS1 / PS1) + W2 x (GS2 / PS2) + ... ]
/( W1 + W2 + … ) (≤ 1)
“Given Percentage …” in BbLearn = 100 x “Given Fraction …” in BbLearn
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
7
Given Percentage of the Weighted
Possible Score Calculations in BbLearn
The “Given Percentage of the Weighted Possible
Score“ in BbLearn is NOT a Fraction of any Whole.
= 100 x [ W1 x (GS1 / PS1) + W2 x (GS2 / PS2) + ... ]
/( W1 + W2 + … )
≠ 100 x (W1 x GS1 + W2 x GS2 + …) / (W1 x PS1 + W2 x PS2 + ...)
It is the Weighted Total of the Given Scores Scaled
by the Possible Scores.
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
8
The Sum of Weighted Ratios is
not the Ratio of Weighted Sums.
𝐺𝑆1
𝐺𝑆2 𝑊1 × 𝐺𝑆1 + 𝑊2 × 𝐺𝑆2
𝑊1 ×
+ 𝑊2 ×
≠
𝑃𝑆1
𝑃𝑆2 𝑊1 × 𝑃𝑆1 + 𝑊2 × 𝑃𝑆2
𝑊1 + 𝑊2 = 1
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
9
The Given Percentage of the Weighted
Possible Scores in BbLearn Is:
[ W1 x (GS1/PS1) + W2 x (GS2/PS2) + ... ]/(W1+W2+…)
• Defined without a sense of the Given Part of a
Possible Whole
• A weighted sum of scaled scores (≤ 1)
• A numerical fraction, that is, a number less than one,
but not a physical fraction, that is, the ratio of two
physical quantities
• Unwittingly, used as a Percentage in BbLearn
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
10
The Given Percentage of the Weighted
Possible Scores in BbLearn
• Is NOT the same quantity that most people
would calculate as the Given Percentage of the
Weighted Possible Scores
• Does ranks students in the same order as the
true Given Percentage of the Weighted
Possible Scores
• If you are going to use the weighted scores
from BbLearn, make sure you tell your
students how to calculate them.
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
11
Given the Way Bb Learn Calculates
the Given Percentage of
the Weighted Possible Scores,
How Does Bb Learn Calculate the
Total Weighted Given Score?
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
12
Total Weighted Given Score
Calculation in BbLearn
“Total Weighted Given Score“ in BbLearn
= “Given Fraction of the Weighted Possible Scores" in BbLearn
x Total Weighted Possible Score
where:
Total Weighted Possible Score
= ( Weight1 x PossibleScore1 +
Weight2 x PossibleScore2 + ... )
/ ( Weight1 + Weight2 + … )
= ( W1 x PS1 + W2 x PS2 + … )/(W1 + W2 + … )
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
13
Shouldn’t these Similar Quantities
be Calculated the Same Way?
Total Weighted Possible Score
= ( W1 x PS1 + W2 x PS2 + … )/(W1 + W2 + … )
in Bb Learn and in General
Total Weighted Given Score
= ( W1 x GS1 + W2 x GS2 + … ) / (W1 + W2 + … )
in General but NOT in Bb Learn!
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
14
Weighted Given Score Calculation
in BbLearn
Total Weighted Given Score in General
= ( W1 x GS1 + W2 x GS2 + … ) / (W1 + W2 + … )
≠ “Total Weighted Given Score“ in BbLearn
= “Given Fraction of the Total Weighted Possible Score”
x Total Weighted Possible Score
= [W1 x (GS1 / PS1) + W2 x (GS2 / PS2) + ...]
x (W1 x PS1 + W2 x PS2 + …)
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
(≤ 1)
15
Weighted Given Score Calculations
in BbLearn
The Total Weighted Given Score calculated in
BbL from the Given Percentage of the Weighted
Possible Scores calculated in BbL should NOT be
used because it is NOT an accurate indicator of
this quantity and should NOT be used in
subsequent Grade Center calculations because it
is NOT a Sum of the Weighted Given Scores!
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
16
Inconsistencies in BbLearn Definitions
• The Given Fraction (Percentage) of Weighted
Possible Scores in BbLearn is NOT defined (or
equal to) a ratio of a given part to the
maximum possible (the whole).
• The Total Weighted Given Scores is NOT
defined in the same form as the Total
Weighted Possible Scores, so the defined
given part is not part of the defined whole.
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
17
Calculations with Categories
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
18
Calculations with Categories
in BbLearn
• Scores in Categories are automatically
combined in two available ways:
– "Equal" (“sized” using scaled scores)
– "Proportional" ( “to what?” using unscaled scores)
• Given Score Scaled by its Possible Score
= GS1/PS1 (≤ 1)
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
19
Scores in Categories Combined Equally
Default
• Score = (GS1/PS1 + GS2/PS2 + …) / N
x (PS1 + PS2 + …) / N
• Fraction = (GS1/PS1 + GS2/PS2 + …) / N
(≤ 1)
(≤ 1)
• Scaled Scores—Not Scores--are Equally Combined.
• Each Scaled Score has a maximum value of 1.
• Unfortunately, the percentage is not calculated as the
ratio of a part to a whole.
• Inconsistently, this Score calculation is the same as the
Percentage calculation for Weighted Columns.
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
20
When all Possible Scores
in a Category are Equal
• The Given Score for the Category is the
Average of the Given Scores.
– Equally Combined Score = (1/N) (GS1 + GS2 + …)
• The “Given Fraction of Possible Scores of the
Category” is the Given Fraction of Possible
Scores of the Category in General.
– Equally Combined Fraction = (GS1 + GS2 + …) / (N x PS)
– PS1 + PS2 + … = N x PS
– Equally Combined Percentage = 100 x … Fraction
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
21
Scores in Categories Combined
Proportionally
• Score = (GS1 + GS2 + …) / N
• Fraction = (GS1 + GS2 + …) /
(PS1 + PS2 + …)
(≤ 1)
• This is the same calculation used for Total
Columns.
• These are physically reasonable quantities
except for the division by N to give an average.
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
22
When all Possible Scores
in a Category are Equal
• The Given Score for the Category is the
Average of the Given Scores.
– Proportionally Combined Score
= (1/N) (GS1 + GS2 + …)
• The “Given Fraction of Possible Scores of the
Category” is N times the Given Fraction of
Possible Scores of the Category in General.
– Proportionally Combined Fraction
= (GS1 + GS2 + …) / (N x PS)
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
(≤ 1)
23
Weighted Score Calculations in
BbLearn Could Be Less Problematic
• BbLearn should calculate weighted scores using general
(simple) weighted sums of Given or Possible Scores.
• Given Fractions (Percentages) of Weighted Possible
Scores should be simple ratio of the Weighted Given
Scores over the Weighted Possible Scores.
• The default combination of scores in categories should
also be a simple sum of scores—not an average.
• Instructors wishing to weight Given Fractions of
Possible Scores can easily do so by adjusting weights.
• An alternative (flagged) combination of scores in
categories and in weighted calculations could combine
Given Fractions of Possible Scores.
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
24
Weighted Score Calculations in
BbLearn Could Be Less Problematic
• You cannot use Categories to automatically sum
the Given Scores in a Category without first
somehow scaling them.
• Bb Learn needs a way to do calculations with all
raw scores by default and with scaled scores as
an option.
– … + W1 (GS1/PS1 + …) + …
scaled scores
– … + W1 (GS1 + …)/(PS1 + …) + … scaled categories
– … + W1 (GS1 + …) + … unscaled scores and categories
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
25
Michael G. Prais, Ph.D.
Academic Computing and Communication Center
University of Illinois at Chicago
mgprais@uic.edu
17 September 2014
Weighted Total Grade Calculations in
Blackboard Learn
26