puzzling maths question
hey!
27 people do a puzzle and the mean time is 22.5 minutes.
Adam and Beth do the puzzle. a>b. When their times are included with the others, the median time increases but the mean time does not change. Suggest possible value for a and b.
Bit stuck on this one - let me know if you figure it out!
27 people do a puzzle and the mean time is 22.5 minutes.
Adam and Beth do the puzzle. a>b. When their times are included with the others, the median time increases but the mean time does not change. Suggest possible value for a and b.
Bit stuck on this one - let me know if you figure it out!
Well to start off, if the mean time doesn’t change, then the mean of the two times must be the same as the mean of the 27. (So (a+b)/2 = 22.5, or alternatively a and b are either side of 22.5 by the same amount)
I think the median thing is more difficult to interpret and doesn’t really give a definite mathematical expression (not that I can see anyway). Here’s what I take from that:
-Median time increases, so both values are above the old median.
- The most likely values for both to be above the median are when the time taken for Beth to do the puzzle (lowest value) is at it’s maximum.
- a and b are relatively close to 22.5, so perhaps 22.3 and 22.8...?
Where is this question from?
I think the median thing is more difficult to interpret and doesn’t really give a definite mathematical expression (not that I can see anyway). Here’s what I take from that:
-Median time increases, so both values are above the old median.
- The most likely values for both to be above the median are when the time taken for Beth to do the puzzle (lowest value) is at it’s maximum.
- a and b are relatively close to 22.5, so perhaps 22.3 and 22.8...?
Where is this question from?
Original post by JGLM
Well to start off, if the mean time doesn’t change, then the mean of the two times must be the same as the mean of the 27. (So (a+b)/2 = 22.5, or alternatively a and b are either side of 22.5 by the same amount)
I think the median thing is more difficult to interpret and doesn’t really give a definite mathematical expression (not that I can see anyway). Here’s what I take from that:
-Median time increases, so both values are above the old median.
- The most likely values for both to be above the median are when the time taken for Beth to do the puzzle (lowest value) is at it’s maximum.
- a and b are relatively close to 22.5, so perhaps 22.3 and 22.8...?
Where is this question from?
I think the median thing is more difficult to interpret and doesn’t really give a definite mathematical expression (not that I can see anyway). Here’s what I take from that:
-Median time increases, so both values are above the old median.
- The most likely values for both to be above the median are when the time taken for Beth to do the puzzle (lowest value) is at it’s maximum.
- a and b are relatively close to 22.5, so perhaps 22.3 and 22.8...?
Where is this question from?
I've attached the full question in case it helps - part g is "Without carrying out any further calculation, explain why the standard deviation of all 29 times will be lower than your answers to part d" - the question is a revision question from Edexcel's data interpretation section for A Level.
Original post by JGLM
Well to start off, if the mean time doesn’t change, then the mean of the two times must be the same as the mean of the 27. (So (a+b)/2 = 22.5, or alternatively a and b are either side of 22.5 by the same amount)
I think the median thing is more difficult to interpret and doesn’t really give a definite mathematical expression (not that I can see anyway). Here’s what I take from that:
-Median time increases, so both values are above the old median.
- The most likely values for both to be above the median are when the time taken for Beth to do the puzzle (lowest value) is at it’s maximum.
- a and b are relatively close to 22.5, so perhaps 22.3 and 22.8...?
Where is this question from?
I think the median thing is more difficult to interpret and doesn’t really give a definite mathematical expression (not that I can see anyway). Here’s what I take from that:
-Median time increases, so both values are above the old median.
- The most likely values for both to be above the median are when the time taken for Beth to do the puzzle (lowest value) is at it’s maximum.
- a and b are relatively close to 22.5, so perhaps 22.3 and 22.8...?
Where is this question from?
p.s. thank you for your help so far anyways!
Original post by tigress22
p.s. thank you for your help so far anyways!
I think what I suggested still works but working with that data would have made it much less complicated xD
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