Maths Homework

[ruggief]

Hi all. How would you answer this question in order to get four marks. It's a year 9 question.
Many thanks

The number of runners in the London Marathon on 25th April 2010 was 37,527. Work out an estimate for the number of runners who's birthday was on that day.

[sunny-dave]

The obvious answer is 37527/365 and rounded = 103

[sunny-dave]

... but - it should probably be divided by 365.25 (allow for leap years) and then an even more accurate figure would be to look at the pattern of births through the year and see if 25th April was higher/lower than the average.

[sunny-dave]

37527/365.25 = 102.74

So that still rounds to 103.

... but ... I think more people will have applied for the marathon who were born on 25th April - as a sort of 'celebration' - so the number is probably higher ...

[sunny-dave]

I may be over-thinking this :+)

[ruggief]

Thanks so far. That's what my daughter started with which is fine for one mark but it's worth 4? Thinking it must be probability question to do with 1:365 to start with plus the same though more would choose that date for a milestone achievement 18th, 50th etc so higher probability but how to calculate to get 4 marks?

[JJ109]

Sunny - what about the people who didn't run in the marathon as it was their birthday and they wanted to celebrate elsewhere.

I would just stick to the maths assumimg that each day is the same.
(Although it is appreciated that the commonest birthdays are 9 months after New Year's Eve)

[Peter Pedant]

yeah point out who's should be 'whose'

define your assumptions ( given data is assumed to be accurate) - not a leap year and each birthday has an equal number -
and you need to round UP

later on you need to suggest improvements in the estimate - use 365.25 and estimate the variation in the number of people with same brithday. ALl you need to know at this level is that it is related to a measure called standard deviation

[JJ109]

I suspect that confidence intervals are probably required to get the other marks. BUT I have long since forgotten how to do those.

[margarettom]

Confidence intervals are too advanced for year 9. I think you get 1 mark for p=1/365
1 mark for 37527/365
1 mark for answer to decimal places and
1 mark for rounding up correctly
This is presuming they can use a calculator to do the division.

[Old_Geezer]

Think I'd settle for one mark, more onto the next question, and finish and be out in the sun while there's still time.

[fiction-factory]

I think margarettom is close to the reasons for the 4 marks. It's possible there is one mark for either recognising that the question included a spelling mistake (who's) or for using 365.25 rather than 365. It's possible some reference to standard deviation/variance might be expected if it's Statistics GCSE although in this case no data has been provided to help calculate the SD

[zebo]

The probability of two people having the same birthday isn't 1/365, in a group of 365 people that would mean that everyone would probably have different birthdays. I can't recall the mathematics of it and for Year 9 it's probably 1/365 but I'll drive myself mad trying to find out the true answer!

[fiction-factory]

Are you thinking that some dates are more likely than others (probably true- I will look), or about the birthday paradox where in a room of 23 people there is a 50% chance of two people somewhere in ther sharing a birthday (although this isn't relevant to this maths question)

[jim360]

I think a few people are overthinking this. I endorse margaret's answer and mark assignment.

[fiction-factory]

This shows the data by date over ayear. Maybe the class were given this extra info?
https://www.panix.com/~murphy/bday.html

[margarettom]

Year 9 tends to be pre GCSE which is usually years 10 & 12 and, as I think this is a probability question, SD would not come into it. Also, 2010 was not Leap Year, so 365 days.

[fiction-factory]

I agree margaret tom- apart from your leap year point which isn't relevant (unless all the applicants were under a year old)- it's all the previous leap years that matter as we are looking at dates of birth.
Anyway, if it was just a homework question I wouldn't worry too much about justifying the mark scheme- I think most would either get it right or get nowhere near the 'right' answer

[margarettom]

You're right about the Leap Year fiction-factory. I lost the plot there.

[fiction-factory]

Year 9s are nearly year 10 now and some top set Maths students will be doing a Statistics GCSE next year which would cover confidence intervals.
I still doubt though that is any more than a simple 37527/365 or 37527/365.25 question.
Just thought- I think some asterisked GCSE questions still give one mark for the written communications, so some words need to be written to explain the calculation and explain the result. Maybe this is the cas eon this homework question

[New Judge]

"This is presuming they can use a calculator to do the division."

Why on Earth, at age around 14 or so, would you need a calculator to perform such a simple calculation?