Q1QP2 Question. 82 ambiguity due to the use of the word "possible"

[Pranav Balakrishnan]

I have a doubt regarding one of the questions in the maths paper. I hope that someone can clear it.

In question 82, it was mentioned: "Choose the possible correct options",
Since both m and n can be unique for example m can be 7 and n can be 9 as has been mentioned in one of the options as well, shouldn't the 6th option (both m and n are unique) be a possible option too?

[Kartik mittal]

But as the first option m=3 and n=3 is correct and both have value 3 so m and n need not to be unique they can be unique for that particular value or scenario but overall they cannot be unique for evey case.

[Pranav Balakrishnan]

They asked us to choose the possible correct options. @Kartik Are you telling me that m and n cannot be unique? I just highlighted one possible scenario in which m and n can be unique. So please explain to my why it is not possible.

Thanks

[Kartik mittal]

I dont think that possible here means that we can apply the condition on only one case.The answer for universal set will be not unique as the condition of uniqueness is not followed by the case m =3 and n=3 and that case only makesnthe whole condition of uniqueness false.

[Pranav Balakrishnan]

@Karthik But where have they mentioned universal set and all. We were asked to select the possible options. By your logic m=n=7 is also not possible because it doesn't talk about the universal set. 

[Pranav Balakrishnan]

@Karthik To further clarify, are you saying that m=n=7 is the universal set? According to your logic, how can option 1 be correct and not option 6?

[Malabika Guha Mustafi]

@Pranav , when both are unique , it means  that uniqueness should be applicable for all cases. But, when m=n=3 and condition is true then it can not be the condition of uniqueness. Kartik explained correctly. Here , universal set means the logical representation of all cases.

[Pranav Balakrishnan]

@Malabika What I am saying is that both can be unique. Both m and n are unique are what the option said. What my point is that m and n can be unique. If they can be unique why is it that that option is not correct. Can m and n, not both be unique? Also, I know what a universal set means. That term has not been used in the question anywhere. I was brought up here in this forum. It was not specifically mentioned in the question paper. 

[Malabika Guha Mustafi]

Yes, if it was said that both could  be unique then definitely 6 th option was correct. But it was mentioned as both were  unique means the conditions of uniqueness should be considered in each case.

[Pranav Balakrishnan]

@Malabika m and n can be unique in some cases and not unique is some other case. Both cases are possible. "Both m and n are unique" This is certainly a possibility and our task according to the question was to find the possible correct options

[Pranav Balakrishnan]

@Malabika So for m=n=7 did they say that that could be true? They never used the word "could" in any options. So how can you insist that they sould say could for just one option

[Malabika Guha Mustafi]

For m=n=3 ,it is true since it satisfies the condition. But not only one option which satisfies the condition.  But if we say they are unique then it is not true since not satisfying the all condition. it is a general statement so to be proved true , it needs to satisfy all conditions.

[Pranav Balakrishnan]

@Malabika You claim that it is a general statement. But how can you simply make that statement. The option did not read "In general, Both m and n are unique". It only said that "Both m and n are unique" which is certainly possible. You can't simply assume that is a general statement. 

[Pranav Balakrishnan]

"Both m and n are unique" can in certain cases satisfy the conditions required by the question. So m and n being unique can satisfy the question just like how m=7 and n=3 can also satify. 

[Sidisha Barik]

I agree. Since the question has used the word possible, it is ambiguous. And since there is a possibility of m and n both being unique, it should also be considered as a correct option.

[Infinity Facts]

I dont think that question has any ambiguity as it is easily understandable bcz options have only one statement regarding uniqueness i.e. "both m and n are unique" . ...if the options contains other statement that "both m and n are not unique"  then it would be ambiguos... But considering the options you have to only check whether the m and n are unique in every case or not....

[Pranav Balakrishnan]

@Kartik How does having another option that says m and n are not unique make the question more or less ambiguous. How can you simply assert that m and n have to be unique in all the cases for it to be correct? Nothing like that has been mentioned in the question nor in the options. Where was it said that both m and n have to be unique in all cases? The options state that both m and n are unique and the question requires us to check which of the given 6 options are "possible". Both m and n being unique are certainly possible and this should also be correct. If it is not mentioned that the options should be true for all cases then how can you insist that that option should be valid for all cases and it is only ambiguous if another option is also given?

[Kartik mittal]

If both the options i.e. "both m and n are unique" and "both m and n are not unique " were there in the answers then your thinking would have been correct but as there is only one option regarding uniqueness it is understandable that the condition is asked for the whole set not for individual cases .....🙏🙏 

[Pranav Balakrishnan]

@Kartik I don't think that you understand what I am trying to say. I certainly understand the words that you have written there. But, unfortunately, I fail to see how my point of view is inconceivable. All I was trying to say was that the inclusion of the word possible has made the question interpretable in multiple ways. I interpreted it in a certain way and this discussion has not made me doubt my interpretation. So I certainly feel that the question was ambiguous. I wish that I could better explain my point of view but unfortunately at this juncture, I think that it is not possible. I thank you for trying to clear my doubt and I am grateful for your effort.

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[Kartik mittal]

I also know what you are trying to say but i am not able to tell you my perspective clearly
The question might be ambiguos but in my view its not...The rest is on iitm.

Welcome and thank you for listening to my points..

[Malabika Guha Mustafi]

@ Pranav,

 Now I am supporting your argument.

In stat set q1,(Question: 68)

Two options are selected as right options which is not supporting the question directly but since "the can  be possible true" argument is there so it is considered correct.

With the same logic,   that both are uniques also should be considered true.

[Pranav Balakrishnan]

Statistics Week 3 Practice Assignment Question Number 10

In this question, both the 7th option "The mean of the data could be any value in the range of [41.133, 53.65]"  and the first option ie. "The mean is 41.1333" are correct. Here, based on the given data we cannot definitively say that the mean is 41.1333 as the data given in the question is insufficient to make that claim, but it(41.1333) is a possible solution as it is a part(subset) of the solution set([41.133, 53.65]). So here since they said "which of the following statements could be true" in the question, we were required to mark the first option also even though it is not a universal solution. So,  when the question asked us to  "choose the possible correct options", "both m and n are unique" even though it is not true for the entire solution set, it is true for a subset of the solution set and can therefore be considered a possibly correct.

[Malabika Guha Mustafi]

Yes, agreed. If we need to take universal set for maths then it should be applicable for statistics also. 

[amrit raj]

I have not given this set of question. Can you post the question here for plausible explanation. ?

Also, just guessing: m and n are unique can also mean that , m and n have only one unique plausible solution/value.

[Malabika Guha Mustafi]

[Rahul Kumar]

here , the option "both m and n are unique" means that exactly only one value of m and n can be possible .But here more than one values are possible as we can observe by the equation. Hence it should be correct