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https://postimg.cc/image/9d9n4o6l7/ I do understand that we need a number in order to work out mean and variance but why does >=6 have to become 7, what’s wrong with 6 or 5?

Reply 1

Gregorius

14

Original post by Angels1234

https://postimg.cc/image/9d9n4o6l7/ I do understand that we need a number in order to work out mean and variance but why does >=6 have to become 7, what’s wrong with 6 or 5?

This is a bit of a fiddle to get the question to be answerable, but there's some sense in it.

Just eye-balling the data, that looks as though the data you're given will be fit by a Poisson distribution with mean in the range 3.5-4. If we take 4 as an example, then the mean of those values from such a Poisson distribution that are greater than or equals six is approximately seven - so the number they've chosen makes sense.

Reply 2

Angels1234

OP

14

Original post by Gregorius

This is a bit of a fiddle to get the question to be answerable, but there's some sense in it.

Just eye-balling the data, that looks as though the data you're given will be fit by a Poisson distribution with mean in the range 3.5-4. If we take 4 as an example, then the mean of those values from such a Poisson distribution that are greater than or equals six is approximately seven - so the number they've chosen makes sense.

If the outer ends are open ended can we assume it has double the interval of the others ? And then to work out the mean we obviously need a whole number so can we take the midpoint of the interval ? What if we are given discrete data but all of the intervals are different and the last one is open ended how would we know what number to pick when calculating the mean

(edited 5 years ago)

Reply 3

Gregorius

14

Original post by Angels1234

If the outer ends are open ended can we assume it has double the interval of the others ? And then to work out the mean we obviously need a whole number so can we take the midpoint of the interval ? What if we are given discrete data but all of the intervals are different and the last one is open ended how would we know what number to pick when calculating the mean

This is one of those questions to ask of those who actually teach at this level - as it appear to me that many of these types of ad-hoc procedures may be specific to exam boards!

If you want a mathematical answer to how to do this sort of thing in general - then it boils down to a case-by-case analysis of how the distribution of values is likely to behave in the open ended categories. So for a discrete distribution (like the Poisson) you can use the exactly specified data to come up with an approximation to the Poisson parameter - and from that you can infer an approximation to the mean value in the open ended category. Similarly, if you have a continuous distribution (like the Normal), with data given in categories of values you can use the exact categories to approximate the normal parameters and then infer the means in the open-ended categories.

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