Question

Two upper level math classes are given a test. There are 10 students in Class A and 10 students in Class B. Both classes score an average of 80% on the test, but the scores for Class A are noticeably different from the scores in Class B. Can you please show me a sample set of test scores for Class A and Class B.

Explain how you determined the scores for each class (and how they are noticeably different) ???? I am very confused.

Find the median of each Class. Show and explain

Which class would you prefer? Explain.

Answer 1

There could be a difference in the distribution of the scores for the 2 classes even when the 2 classes have the same average score. This can be shown by the following example:

• Class A: 60%, 60%, 60%, 60%, 60%, 100%, 100%, 100%, 100%, 100%
• Class B: 79%, 80%, 80%, 80%, 80%, 80%, 80%, 80%, 80%, 81%

We can see above that for both cases, the class average is the same that is 80%, but the spread of the marks in Class A is much larger than in class B.

The median for Class A is computed as the middle value of the 5th and 6th class that would be 80% here.

Similarly for Class B, the middle value for 5th and 6th would be 80% as both 5th and 6th values are equal to 80%

We would clearly prefer class B as there is lesser spread in that class and almost all students have performed well.

We always prefer things with a lower standard deviation ( measure of spread )