Since we cannot be 100% sure which test Frank did better on, we need to find a way to make the comparison doable. This can be done by converting Frank's score to the standard score (or also known as the z-score).
The z-score is calculated through the following formula:
[tex]Z= \frac{X-mean}{deviation} [/tex] where X is Frank's original score.
Converting Frank's scores to a standard score accounting for both the mean and standard deviation of the population who took the test will make the comparison possible.
We get the following z-scores after conversion:
[tex]Z_{Bio}= \frac{55-60}{10} =-0.5 [/tex]
[tex]Z_{Chem}= \frac{70-80}{15} =-0.67 [/tex]
If you read up more on the concept of z-score, you may know that this score just means the amount of standard deviations a data falls with respect to the mean. Comparing Frank's two scores, we can see that they are both below the mean. However, it can be seen that Frank's z-score for his chemistry test is lower than his z-score for his biology test.
This suggests that Frank scored relatively poorer in chemistry than he did in biology.
ANSWER: Frank did better in his biology test.
