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Data set \(S\) consists of positive numbers. If -1 is added as an element to set \(S\), which of the following is NOT possible?

A. The mean will decrease but median will not change. B. The median will decrease but mean will not change. C. The range will increase but median will not change. D. The range will increase but mean will decrease. E. The standard deviation will increase but mean will decrease.

Data set \(S\) consists of positive numbers. If -1 is added as an element to set \(S\), which of the following is NOT possible?

A. The mean will decrease but median will not change. B. The median will decrease but mean will not change. C. The range will increase but median will not change. D. The range will increase but mean will decrease. E. The standard deviation will increase but mean will decrease.

The mean of set \(S\) is \(\frac{sum}{n}\), where \(n\) is the number of terms in set \(S\).

Since set \(S\) consist of positive numbers, then when we add -1 to the set the sum of the numbers in the new set will decrease. So, the new mean will be \(\frac{\text{less sum}}{\text{more terms}}=\frac{\text{less sum}}{n+1}\), which will be less than \(\frac{sum}{n}\). Hence the mean must decrease.

Sure, mean will definitely decrease as explained. However, how is it possible that median can stay the same (as answer choice A suggests) even after -1 has been added to this set of only positive numbers? Can someone come up with an example to show that? Thanks.

Sure, mean will definitely decrease as explained. However, how is it possible that median can stay the same (as answer choice A suggests) even after -1 has been added to this set of only positive numbers? Can someone come up with an example to show that? Thanks.

If S={1, 1, 1}, then the median is 1. Adding -1 we get S'={-1, 1, 1, 1}, the median is still 1.
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I think this question is good and helpful. I think there is an error in the answer. As the explanation said, the mean must decrease and the answer "B" says that the mean will not change. The correct answer is "D"

I think this question is not helpful. answer B says that mean will not change-so the answer should be A?(mean decrease)

hi the question asks what is not possible? and if you add a negative number to a set of positive number, the mean will decrease... ans B says it will remain the same, which is not possible... therefore ans B...
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Hello, for the below question mean will decrease. 1. Range will increase 2. Standard deviation will decrease.

How do we conclude about median for this case?

option E is also impossible.

Please clarify.

Regards, Mahuya

Set \(S\) consists of positive numbers. If -1 is added as an element to set \(S\), which of the following is impossible?

A. The mean will decrease but median will not change. B. The median will decrease but mean will not change. C. The range will increase but median will not change. D. The range will increase but mean will decrease. E. The standard deviation will increase but mean will decrease.

The mean of set \(S\) is \(\frac{sum}{n}\), where \(n\) is the number of terms in set \(S\). Since set \(S\) consist of positive numbers, then when we add -1 to the set the sum of the numbers in the new set will decrease. So, the new mean will be \(\frac{\text{less sum}}{\text{more terms}}=\frac{\text{less sum}}{n+1}\), which will be less than \(\frac{sum}{n}\). Hence the mean must decrease.

Hello, for the below question mean will decrease. 1. Range will increase 2. Standard deviation will decrease.

How do we conclude about median for this case?

option E is also impossible.

Please clarify.

Regards, Mahuya

Set \(S\) consists of positive numbers. If -1 is added as an element to set \(S\), which of the following is impossible?

A. The mean will decrease but median will not change. B. The median will decrease but mean will not change. C. The range will increase but median will not change. D. The range will increase but mean will decrease. E. The standard deviation will increase but mean will decrease.

The mean of set \(S\) is \(\frac{sum}{n}\), where \(n\) is the number of terms in set \(S\). Since set \(S\) consist of positive numbers, then when we add -1 to the set the sum of the numbers in the new set will decrease. So, the new mean will be \(\frac{\text{less sum}}{\text{more terms}}=\frac{\text{less sum}}{n+1}\), which will be less than \(\frac{sum}{n}\). Hence the mean must decrease.

I think this is a poor-quality question and I agree with explanation. the solution doesnt align with the answer marked as correct. D is the correct answer.

I think this is a poor-quality question and I agree with explanation. the solution doesnt align with the answer marked as correct. D is the correct answer.

what about the SD? the distance between numbers remain the same, thus the SD will not change. only E mentions something about SD, and since SD will not change, E can be a candidate as well. no?

ok, now I see, not -1 to all elements, but -1 added as a new element..yes E can't be true..

I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. The statement after but is dubious...so what should we consider as a statement....

Before the "But" whatever is mentioned is true/ false and after it is False/ True in some cases...

so what should we consider, either meaning before But or after but...as it is contradictory....for example...option C says Range will increase (true)...BUT...Median will not change (it will change as the number of items in the set will change)