How do mean and standard deviation change after discarding outliers?

Question

**Sara measured the time in minutes between cars passing her camp near a desert road over a two hour period

The times she measured were 6, 6, 8, 9, 10, 11, 13, 13, 20, 24.

She calculated the mean and standard deviation for this set of data. (She decided to reject the two outliers (20 and 24)

How do the new mean and standard deviation compare to her original ones?

A The mean and standard deviation both decrease.

B The mean and standard deviation both increase.

C The mean stays the same and the standard deviation decreases.

D The mean decreases and the standard deviation increases.

My answer is A **

hi valtteri thanks for your comment my question is are my answer A is correct < thanks valtteri have a nice day ♥ — Momen Osama, Mar 13 '13 at 17:24
Because if deletes values it will decrease and will decrease total and that lead to decrease the mean, also decrease the dispersion of the values so will decrease the standard deviation > — Momen Osama, Mar 13 '13 at 17:29
yes i think that D is correct < the sentence standard deviation increases , Makes it puzzling between increase and decrease of the standard deviation .thanks valtteri ♥ — Momen Osama, Mar 13 '13 at 17:34
thanks valtteri < now i Confirmed that A is the correct answer — Momen Osama, Mar 13 '13 at 17:38

amWhy · Accepted Answer · 2013-03-13T17:37:36.930

1

Yes, you are correct: and for the reasons you give in your comments, too, [sort of for the mean (the divisor = sample size, will also decrease), but overall the mean will decrease]. As you state, as well, with respect to the standard deviation, the dispersion will certainly decrease without the values $20$ and $24$ removed. And the standard deviation will decrease as a result (the remaining values are more closely "lumped" together).

But it would also be good for you to confirm your answer by testing (computations). That way, you wouldn't need to even ask the question for verification! But it seems you have good enough intuition as to what mean and standard deviation represent, which is sufficient to answer the question as stated!

edited Mar 13 '13 at 17:37

answered Mar 13 '13 at 17:32

amWhy

209,954

thanks amwhy for the answer and i will enjoy this usefull website ♥ ♥ ♥ – Momen Osama Mar 13 '13 at 17:37
Dear Momen: you're welcome! In the future, it really helps us when you post your thoughts, following the question (in the post itself), just as you wrote your thoughts in the comments below your post. That way, we can give you more precisely, the help you need! Welcome to Math.SE! – amWhy Mar 13 '13 at 17:40
Frankly I did not expect to find a website this wonderful experience.And especially I got the answer very quickly, and also I support try the solution or the complete solution when you put the question, because the mathematics scientific material is not literary and use reason and critical thinking, thank you all for this wonderful work , thanks amwhy for your help – Momen Osama Mar 13 '13 at 17:49

How do mean and standard deviation change after discarding outliers?

1 Answers1