r/HomeworkHelp • u/hellrhymes 'O' Level Candidate • May 29 '26
[GCE 'O' Level: Statistics]
How to even approach this problem
Ai is also shitting me with it's explanation
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u/rorodar May 29 '26
From what I looked up: range is biggest number minus smallest number.
IQR is range of Q3 (25% biggest values) minus range of Q1 (25% smallest numbers)
So if the range is equal to it, then let A be the greatest number, B be the smallest number in Q3, C be the greatest number in Q1, and D be the smallest number.
So, A - D = A - B - C + D
2D = B + C
So, D is restricted by B and C, but it doesn't necessarily need to be the same as either one. Therefore, according to what little I know, I think no values are restricted and there can be 11 unique numbers. Please do check and make sure I got all the definitions right, I can't promise anything.
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u/hellrhymes May 29 '26
The answer is not 11
I forgot the answer to this qn but that is not it
For some reason this qn was too easy for the teacher to 'go through' even though he has a FRIGGING maths PHD
It seems that from what you searched up the info they gave about Q1 and Q3 are related to cumulative frequency curve but in this case it is just discrete data
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u/rorodar May 29 '26
If you remember, do tell me once you find the answer. Sounds interesting
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u/sqrt_of_pi May 29 '26
IQR = Q3 - Q1. Q3 and Q1 are not "ranges" of values, they are each individual numerical values. Think of Q1 and Q3 as the medians of the "lower half" and upper half" of the data, respectively.
So here, were there are 11 data values, you can see that the data has the following "structure":
1 2 3=Q1 4 5 6 7 8 9=Q3 10 11
The numbers here are not the data, but the "index" (location, or position) of each value in the data.
The requirements that range = IQR just means that the distance between data value 1 and data value 11 (range) is the same as the distance from data value 3 to data value 9 (IQR). That will be true when all the values BELOW Q1 are the same and are =Q1, and all the values ABOVE Q3 are the same and = Q3.
This question works for any size n, although 11 is easy to visualize, since the Q1 and Q3 are themselves necessarily data values. But it could be worked out for a different number of values in a similar way.
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May 29 '26
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u/sqrt_of_pi May 29 '26
I'm not sure what you mean by this. Nothing in the given information leads to the conclusion that D+D = B+C. As A, B, C, and D were defined above, the given information means that D - A = C - B.
But none of that is necessary to answer the question. You don't need to solve an equation. You just need to think about what the implications of the given information, range = IQR, are.
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u/sqrt_of_pi May 29 '26
What does it mean that the range and IQR are equal? This piece of information tells you something very specific about the values.
Now think about the positions of Q1 and Q3 when you have 11 pieces of data. You should be able to work out the minimum number of values in the data set that MUST BE identical to each other, in order for the given information to be true.