## Learn@UW - Possible Problems with Calculation Quiz Questions Being Mis-Graded

Under certain conditions it is possible that a correct answer to an Arithmetic or a Significant Figures quiz question may be marked as incorrect.

### Possible Problem with Answers to Arithmetic Questions Off the Correct Answer by Exactly the Specified Tolerance

If an answer specified to an arithmetic question differs from the correct answer by exactly the specified absolute tolerance, it may be flagged wrong.

A problem may occur if the tolerance is plus or minus 0.5 (= 1/2), and the answer precision is 0 (round to a whole number).

For example, suppose the question is *What is 5/8 of 100 rounded to a whole number?*
The true answer of 62.5 needs to be either rounded up to 63 or rounded down to 62.
Either answer should be marked correct but one or both of these possible answers may be marked incorrect.

#### Recommendations:

- Take care to avoid creating quiz questions where such a 'worst case scenario' may occur where a specified answer is constrained to be off by the value of the tolerance set.
- Alternatively, you can specify a tolerance that is slightly larger to avoid the this problem. For the above example, you could specify a tolerance of 0.51 instead of 0.5.

### Possible Problem with "Plus or Minus One Half of the Least Significant Figure" Tolerance

In a Significant Figures quiz question, if you specify a tolerance of "plus or minus one half of the least significant figure", there is a slight chance a correctly specified answer could be marked incorrect.

This is mostly like when the student taking the quiz, due to the number of significant figures specified for the answer, has to specify an answer that differs from the true answer by one half of the least significant figure, either rounding up or down.

For example, 3 significant figures are called for when answering the question:
*Evaluate 8x10 ^{6} + 5.5x10^{4}.*
The true answer of 8.055x10

^{6}needs to be either rounded up to 8.06x10

^{6}or rounded down to 8.05x10

^{6}. Either answer should be marked correct but one or both of these possible answers may be marked incorrect.

#### Recommendations:

- Take care to avoid creating quiz questions where such a 'worst case scenario' may occur where a specified answer is constrained to be off by one half of the least significant figure.
- Alternatively, you can specify a percent tolerance that is slightly larger than one half of the least significant figure.