[pop000]

The question description is like this: grade distribution in English exam of 60 students is positive asymmetry with average grade 72, the teacher decide to give for any student who got grade that it last than the average more 6 points as a result:
A) the average will get bigger in less than 3 points and the Variance will grow smaller.
B)the average will get bigger in more than 3 points and the Variance will grow smaller.
C)the average will get bigger in less than 3 points and the Variance will grow .
D)the average will get bigger in more than 3 points and the Variance will grow.

How can I solve it?

Thanks and sorry about my bad English

[jcaron2]

If exactly half (30 students) got the 6-point bonus, the average would have increased by exactly 3 points. However, the distribution has positive asymmetry. That means more students scored above 72 than the number below 72. If only the students who scored below average get the extra 6 points, that means fewer than half ( < 30 ) got the bonus. So what does that say about the amount the average will increase?

Concerning variance, we can assume that the 6-point bonus pushed most of the below-average students closer to the average. What does that do to the variance?

I feel I should point out that technically this is a bad question because it's also possible (although unlikely) that the 6-point bonus actually pushed the below-average students further from the average. For example, if 20 students had scores of 71.8, and 40 students had scores of 72.1, the 6-point bonus would have improved the below average students' scores to 77.8. Clearly that is further from the new average than the original scores! However, I think it's safe to assume the teacher would not have given them a bonus in that case. :) I'm just making a point that math teachers should be more careful about constructing non-ambiguous questions.

[pop000]

Hi.
If I Understand you correctly so the average will get bigger in less than 3 points and the Variance will grow smaller.

Thank you for your good answer.

About your point on the technically in this question I will show your example to my teacher I want see what he will say :).

[jcaron2]

Yes, exactly! :)