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## Batman

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#802367 19-Apr-2013 16:18

that is a high school response ... don't sway left and right for "the answer" ... it is a process and you might be surprised at the reasons given by your teacher at arriving at his her "answer"

post "the answer" and go from there

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## stuzzo

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#802408 19-Apr-2013 17:36

I will attempt to refute Nakedmolerat with the following example of 12 students constructed using my argument above.

Maths      Science

4th Quartile  6,5,5        7,7,7
3rd Quartile  5,5,5        5,5,4
2nd Quartile  5,4,4        4,4,3
1st Quartile  3,3,3        3,3,1

Total 53 53

So they can have the same average score after 12 students, go to 16 and the Science average can be higher.

The argument might be over the best way to demonstrate "rated the best" but Nakedmolerat's explanation changes between the subjects, at least average is consistent.

## Batman

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#802429 19-Apr-2013 18:21

stuzzo:

there doesn't seem to be sample size indication ...

will your answer be different if the sample size was different? there could be infinite permutations depending on the sample size which eg if there were 10 in each group

## Batman

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#802430 19-Apr-2013 18:23

stuzzo: I will attempt to refute Nakedmolerat with the following example of 12 students constructed using my argument above.

Maths      Science

4th Quartile  6,5,5        7,7,7
3rd Quartile  5,5,5        5,5,4
2nd Quartile  5,4,4        4,4,3
1st Quartile  3,3,3        3,3,1

Total 53 53

So they can have the same average score after 12 students, go to 16 and the Science average can be higher.

The argument might be over the best way to demonstrate "rated the best" but Nakedmolerat's explanation changes between the subjects, at least average is consistent.

you mean the "mean"

## stuzzo

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#802441 19-Apr-2013 18:32

joker97:
stuzzo: I will attempt to refute Nakedmolerat with the following example of 12 students constructed using my argument above.

Maths      Science

4th Quartile  6,5,5        7,7,7
3rd Quartile  5,5,5        5,5,4
2nd Quartile  5,4,4        4,4,3
1st Quartile  3,3,3        3,3,1

Total 53 53

So they can have the same average score after 12 students, go to 16 and the Science average can be higher.

The argument might be over the best way to demonstrate "rated the best" but Nakedmolerat's explanation changes between the subjects, at least average is consistent.

you mean the "mean"

The sample size was given as twelve students. The argument was simply to find a case where the Science mean score could be the same or higher than Maths.

Yes mean/ average, I've forgotten if there's a distinction.

## sonyxperiageek

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#811742 5-May-2013 20:17

nakedmolerat:

Easy

a) Maths rated the BEST - most students gave score 4-5 (you need to imagine the box-plot as histogram or area under the graph to understand this better). English is the second best as they have median value higher than Science. English is not the best because the number of students who like/dislikes the subject is spread out more than maths.

b) Both median and upper quartile is 5 whilst the lower quartile is 4. This means 50% of the students choose score of 4 and 5. From that group more than 50% of them chose score of 5 (or more than 25% overall).

Hi nakedmolerat, I just got this answer below, do you think it's right? Thanks again!

A) English and maths were rated the same and this is represented by the same median for both. This means that 50% rated them the same. However English had a higher upper quartile but a wider spread, indicating the large varying opinions of the students.

B) The box is represented by 3 lines, the upper quartile, median and lower quartile. In the case of the maths box, the value of the median was also the same as the value of the upper quartile therefore it was only represented by two lines the upper quartile/median and the lower quartile.

Sony

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## nakedmolerat

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#811744 5-May-2013 20:26

Yea that sounds right

## sonyxperiageek

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#811748 5-May-2013 20:32

So maths and english are rated the same?

Sony

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## nakedmolerat

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#811750 5-May-2013 20:36

Yes because the median score is the same. I didn't think of that earlier

## Batman

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#811813 5-May-2013 23:14

You see however hard we argued we were All wrong according to your teacher

## sonyxperiageek

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#811833 6-May-2013 06:56

That answer wasn't from my teacher, just another friend. I wouldn't be clarifying the answer with nakedmolerat if my teacher gave me that answer.. :P

Sony

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## bazzer

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#812754 7-May-2013 13:01

I don't believe it's a right/wrong kind of question. It just requires you to justify your answer, which you could pick from a range of right-ish answers.

## wellygary

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#812836 7-May-2013 14:08

bazzer: I don't believe it's a right/wrong kind of question. It just requires you to justify your answer, which you could pick from a range of right-ish answers.

+1, the question asked which was rated the "best", now it is a subjective judgement of what "best" is

Your quantitative answer ( the median) is the same., so ou are being asked to justify a "best" based on other information (spread, highest and lowest outliers etc) and there is no single position on which of those is more important in defining "best"

## stuzzo

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#812841 7-May-2013 14:14

English and maths were rated the same and this is represented by the same median for both. This means that 50% rated them the same.

Having the same median doesn't mean that 50% rated them the same, it means that 50% rated them five or higher for both subjects.

This question is obviously looking for a qualitative reply that indicates that you can understand and interpret the graphs. Unfortunately, like much woolly maths done at this level, it doesn't provide enough information to give an exact answer, it's all in how you define "rated the best"' and, ironically, is likely to trouble the cleverer kids.

In my opinion, that is best given by the mean which, as I have shown, could be higher in any of the subjects. They are unlikely to want you to think about the mean though.

The best thing is to define, first, what you think "rated the best" might mean and form an answer from that.

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