Why can’t you simply average two accuracy rates?
Suppose you take a safety knowledge quiz: Group A has 10 people, 9 answer correctly, for an accuracy rate of 90%; Group B has 90 people, and 9 also answer correctly, for an accuracy rate of 10%. Add 90% and 10%, then divide by 2, and you get 50%. But across both groups, only 18 out of 100 people answered correctly, so the overall accuracy rate is actually 18%.
The problem is that the groups are very different in size. Simply averaging the two percentages treats the group of 10 as equal in weight to the group of 90. To combine proportions like these, first add the number of correct answers, then divide by the total number of people. Don’t focus only on the two prominent percentages on the page.
When you see “average accuracy rate” or “average pass rate,” take a closer look: How many people are in each group, and is the calculation method clearly explained? If you’re given only proportions, with no corresponding group sizes, keep a question mark in mind. This is a hypothetical example, not the result of a real test.
#数据常识 #Study Notes
Suppose you take a safety knowledge quiz: Group A has 10 people, 9 answer correctly, for an accuracy rate of 90%; Group B has 90 people, and 9 also answer correctly, for an accuracy rate of 10%. Add 90% and 10%, then divide by 2, and you get 50%. But across both groups, only 18 out of 100 people answered correctly, so the overall accuracy rate is actually 18%.
The problem is that the groups are very different in size. Simply averaging the two percentages treats the group of 10 as equal in weight to the group of 90. To combine proportions like these, first add the number of correct answers, then divide by the total number of people. Don’t focus only on the two prominent percentages on the page.
When you see “average accuracy rate” or “average pass rate,” take a closer look: How many people are in each group, and is the calculation method clearly explained? If you’re given only proportions, with no corresponding group sizes, keep a question mark in mind. This is a hypothetical example, not the result of a real test.
#数据常识 #Study Notes