A certain list of 200 test scores has an average

Thanks Karishma. I ask this question because I am using the method used by many succesful test takers. According to them, you shouldn't evaluate only why the OA is the answer, but also identify why the other choices are wrong. That strategy helpmed a lot, specially in the Verbal section, although I am not so sure whether it is very useful in PS questions.

Thank you Bunuel and Karishma, I have an additional question. In this case, the choice is D because the mean still being 85 after adding the two new elements. But if we add two different elements instead of the two 85s (like in the other choices), the mean will change too. So the individual distances between the mean and the elements (the new and the old ones) will change too. Therefore, we couldn't be so sure that the standard deviation has increased or decreased.

What do you think about that? You don't expect that, do you? LOL

There is a basic difference in Verbal and Quant questions. In Verbal, you are looking for the 'best answer' (Certainly in RC and SC. To a much less extent in CR). In Quant, you are looking for the 'only possible answer'. When you get an answer of 5 m/hr to a TSD question, you do not question why the other options (4 m/hr or 8 m/hr) are not correct.

GMAT doesn't give you a calculator in Quant so it doesn't expect you to do long calculations. The answer will be logical as in this case. They will not give you options in which you will need to calculate each and find out.

I think, metallicafan wants to validate his logical reasoning in this case. Therefore, here are my 2 cents on this question.

When I did this question, the first question that came in my mind is - What could be the value, which I was assuming, of Standard Deviation. Then, I rechecked the question I found out is value of std deviation should be positive. i.e. no zero and no negative is allowed.

Assume d to be minimum i.e "1" and see the impact of expected data sets on the mean and std deviation, by using the definition and concept that Bunuel provided.

example - Take choice A . 80 and 80, since you have assumed the d to be 1, therefore, adding these two values will increase the mean and hence standard deviation. Therefore, incorrect.

Remember, your task is to stay close to the mean.
Now, check the impact of each n every choice.

Thanks
H

It's all relative. Look for the numbers closest to the mean. The option that adds minimum to the numerator, will be the only one which will reduce d (since there can be only one answer).

If you look at the rest of the options,
(A) 80 and 80
(B) 80 and 85
(C) 80 and 90
(E) 85 and 90

Options (B) and (E) will give the same result so you cannot have both in case option (D) is not there.


(A) 80 and 80
(B) 80 and 85
(C) 80 and 90
(E) 85 and 86

Now answer will be (E)

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Standard deviation is a measurement of how far the values are from the mean

So the smaller the standard deviation it indicates that the values are closer to the value of the mean and the larger the standard deviation, it tells us that the values are farther away from the mean

Keeping this principle in mind, the above set has a mean of 85 and sd = d.

In order to decrease the standard deviation, the two values that we pick must be very close to the mean hence Choice D is the best answer

We know that the average for the given set is 85. Thus, any new value, when added and which is not equal to the average WILL contribute to the S.D. However, if any new value which is added,IS the mean, then the only change will be the increased value (202 in this case from the previous case of 200) in the denominator of the S.D formula. Thus, only option D will ALWAYS keeps the numerator intact and increases the denominator--> Decrease in the overall value for the S.D.

<--SD---Mean--+SD-->


To reduce SD, pick values which are as close to Mean, so 85 is the answer.

I have a question to experts. If the question asks, whats the minimum value added so that we can have max SD, we shall have two answers 1 on either side, right ?
Also such questions may not have any max value to be added, as max value is infinite. Please correct me if mu understanding is wrong.

If you want to increase SD, you will add a value as far away from mean as possible. Say in test scores, if the average is 85 and the maximum marks are 100, the test score that when added will increase SD the most will be 0 (assuming there is no negative marking). 100 is not as far as 0 from the average 85.

And yes, such questions may not have any max value since it may be infinite.

Thankyou for replying.

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