germanivanov0719
commented
1 year ago Math for the calculations
Variables available
Right now, there are a few basic variables. Here is a table with proposed math names (for formulas), descriptions, current (ver. d44e2b0) and future names in code for each:
| Math Variable | Description | Current name | Future name |
|---|---|---|---|
| $M_0$ | Original mean value | M1 |
M0 |
| $W_0$ | Original weight sum | s |
W0 |
| $x$ | New grade value | m |
x |
| $w$ | New grade weight | w |
w |
| $M_1$ | New mean value | M2 |
M1 |
| $W_1$ | New weight sum | Not used | W1 |
Formulas
Let's define basic formulas for variables in the table above.
$$ W_1 = W_0 + w \ \ $$
$$ M_1 = \frac{M_0 \cdot W_0 + x \cdot w}{W_0 + w} $$
From the second formula, we can find $w$:
$$ w = \frac{W_0 (M_0 - M_1)}{M_1 - x} $$
Assuming rounding up to the nearest integer from $M_1$ including (therefore, making it the closest value we have to reach), and only solving for integer values of $w$ (as it is the weight, which is often a whole number):
$$ w = \left\lceil {\frac{W_0 (M_0 - M_1)}{M_1 - x}} \right \rceil $$
What's different
- Make sure to use the correct $M_1$ value when going down (e. g. you need at least $2.49$ to round down, not $2.50$, when using the normal math rounding)
- If $M_1 < M_0$, the $w$ value is still positive, which is different from the current approach. Maybe it is worth getting rid of the negative sign as it may be not that intuitive for someone, and just put a warning or a text label instead.
- If the calculated $w$ is negative, then the input makes no sense. For example, if you are trying to reach $M_1 = 5.0$ with $x = 4$ and $M_0 < M_1$.
- Rounding up (ceiling) is important. Do not use normal rounding or rounding down for this approach.
Opportunities
-
This approach allows the user to specify more conditions for the calculation.
For example, right now you can only use $x = 3$ for calculations, when looking for $M_1$ rounded to $3$. This approach also allows using $2$'s, $1$'s, zeros, and even negative and/or non-integer numbers to reach the same rounded $M_1$ value.
-
It allows users to specify the set of grades their school uses for grading.
It is possible to add a manual entry, or just provide a range selection for users in settings, which would later be displayed on the main page.
-
Calculating will be much faster even for the huge values.
This approach takes approximately constant time, and it means users will be able to recalculate as many times as they want without worrying about performance.
Possible implementations
I'm still thinking about which interface should be used to support most of the features of the new approach. However, it is likely I'll save current view at least for calculations with roundings.
Issue
When creating this app, I used a brute-force approach for calculating required number of new grades to reach a certain goal. While it does allow me to add the option to calculate with rounding, it greatly decreases performance and limits the number of available goals and marks used to reach those goals.
I knew about this design limitation, and it has to be fixed as some point. I will have to come up with a solution on how to integrate the fix to this app.
Status Tracking