Georgie1316
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Hey guys!
I am practicing for the maths professional skills tests and this question has come up.
I would know how to find the median, mode, range from some data, but I have zero idea how to work backwards??

I'm sure there's something simple but I have not come across it before and my brain is not getting there in how to figure it out.

could anyone please advise? The questions below!

Thanks ...




Three classes sat a maths test, which was scored out of 100, and the following statistics recorded.
Image
Indicate all the true statements:
A: In class A, no-one got more than 75 marks.
B: In class C, at least one pupil scored less than 40%.
C: At least one pupil got greater than 85 marks in class B.
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airfixfighter
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I've put the answers below but you need to use the range to figure out the highest and lowest marks. For example, to check A, you need to see what the lowest mark would be for that statement to be true (at least 76 marks with a range of 30 gives a lowest mark of 46) and see if you can figure out from the median and mode if that is the lowest mark.

Spoiler:
Show


A: The range is 30. This means that for someone to have over 75 marks, the lowest result would have to be 46 (46+30 = 76). However, the median and the mode are both lower than 46 so students DID get results lower than 46 so this statement is true.

B: Range is 61. The highest possible score is 100. This means that if a student got 100, the lowest mark would be 39. This is less than 40% (100 marks on the test) and so this statement is true.

C: This is similar to the first one. The range is 24. If a student got more than 85, they got at least 86. This gives the lowest mark to be 62. By looking at the mode, you can see that students got less than 62 and so this statement can't be true.





I hope that's helpful? Let me know if it's not or I've done it completely wrong!
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Georgie1316
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(Original post by airfixfighter)
I've put the answers below but you need to use the range to figure out the highest and lowest marks. For example, to check A, you need to see what the lowest mark would be for that statement to be true (at least 76 marks with a range of 30 gives a lowest mark of 46) and see if you can figure out from the median and mode if that is the lowest mark.

Spoiler:
Show



A: The range is 30. This means that for someone to have over 75 marks, the lowest result would have to be 46 (46+30 = 76). However, the median and the mode are both lower than 46 so students DID get results lower than 46 so this statement is true.

B: Range is 61. The highest possible score is 100. This means that if a student got 100, the lowest mark would be 39. This is less than 40% (100 marks on the test) and so this statement is true.

C: This is similar to the first one. The range is 24. If a student got more than 85, they got at least 86. This gives the lowest mark to be 62. By looking at the mode, you can see that students got less than 62 and so this statement can't be true.






I hope that's helpful? Let me know if it's not or I've done it completely wrong!
HMMM ok thank you for explaining it! i can kind of see what youve done, i checked the answers and you correct with the statements. Just not sure id be able to apply what you did to another one!!
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SarcAndSpark
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(Original post by Georgie1316)
HMMM ok thank you for explaining it! i can kind of see what youve done, i checked the answers and you correct with the statements. Just not sure id be able to apply what you did to another one!!
I'll have a go at explaining how I would do it to see if it helps:

For A: We know the range is 30, so the difference between the highest result and the lowest result is 30 marks. So we take the highest mark we want to check (76) and take away the range (30). 76-30=46. For the statement to be true, 46 would have to be the lowest result.

Now we look at what else we know about the results- the median is 45 and the mode is 42. Obviously we can't have a median and mode lower than the lowest result so the statement is untrue.


For B: The highest possible score is 100. We know the range again is 61. So we can take the highest possible score (100) and take away 61. 100-61=39. 39 is the highest possible lowest score with the data we've been given (I know that's a confusing sentence, sorry!).

As it's 39/100, it would be 39%, so we know the statement must be true.

For C: Like the first statement, we take the result we want to check (86) and take away the range- 86-24= 62. So for the statement to be true, the lowest score in the class would have to be 62.

We know the mode is 60, and we know the mode can't be lower than the lowest possible result, so the statement must be untrue.

Although these questions obviously require an understanding of maths, they're almost like logic questions- you have to work out what needs to be true for the statement to be true, and how to find out if that's possible with the data set.

If you struggle with this type of question, when it comes to the numeracy test you could always leave it until last, so that you have more time to think about it, and don't forget that dropping the odd mark won't make you fail the test.
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Georgie1316
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I passeeedddddddddd
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tom_tom_tom
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Easiest way I worked this out in case anyone else was struggling was. The test is out of 100 therefore all of the figures in the table can be assumed as a percentage.

For these half the range and minus and add that to the median to get the top and bottom figure. As the median falls in the middle of the data you can assume the range will also straddle this evenly.
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