How to infer the smallest possible size of the used sample based on the %?
I'm not a mathematician, so sorry for a confusing title. Let me explain.
For example, I'm shown a pie chart and it is split to 50% and 50%.
So logically, the smallest possible sample to achieve that would be 2. 1 and 1 = 50% and 50%.
What about if I'm given a pie chart with 70%, 15.87% and 14.13%.
How would I find out the smallest possible sample size, for which I could achieve these numbers?
So if someone shows me this pie chart without telling me the sample size, I can find out if their sample size was large enough (let's say it's only possible to achieve such a "precision" by dividing numbers above 500)
I mean naturally, to achieve the numbers I mentioned above, the sample size cannot be small, as you wouldn't achieve such a split with let's say a sample size of 5. The numbers are too "weird" for that (again, sorry for the non-scientific description...)
statistics percentages
asked Nov 25 '18 at 10:28
RadekC
1
|
show 2 more comments
I'm not a mathematician, so sorry for a confusing title. Let me explain.
For example, I'm shown a pie chart and it is split to 50% and 50%.
So logically, the smallest possible sample to achieve that would be 2. 1 and 1 = 50% and 50%.
What about if I'm given a pie chart with 70%, 15.87% and 14.13%.
How would I find out the smallest possible sample size, for which I could achieve these numbers?
So if someone shows me this pie chart without telling me the sample size, I can find out if their sample size was large enough (let's say it's only possible to achieve such a "precision" by dividing numbers above 500)
I mean naturally, to achieve the numbers I mentioned above, the sample size cannot be small, as you wouldn't achieve such a split with let's say a sample size of 5. The numbers are too "weird" for that (again, sorry for the non-scientific description...)
statistics percentages
asked Nov 25 '18 at 10:28
RadekC
1
1
Multiply the values by $100$ to get $7000$, $1587$, and $1413$. Simplify by looking for the greatest common factor and then add up the simplified values.
– KM101
Nov 25 '18 at 10:43
A small addition to @KM101 's comment: you should multiply a value for every part by 10 until you get only integers. So, in an example with 50 and 50, you don't have to multiply anything, while in case of having, say, 50, 33.333 and 16.667, you should mutiply every value by 1000. After that, as it's been said, all you need is to find the greatest common factor for all those values
– Andrei Rykhalski
Nov 25 '18 at 10:50
Thank you so much, that's it! So silly I didn't think of that!
– RadekC
Nov 25 '18 at 10:59
That method don't work. Applied to $50,33.333,16.667$, you get $50000, 33333, 16667$ which have no common factor other than one, so you decide the sample size is $100000$. But in fact the sample size is $6$, it's just that the numbers have been rounded to three decimals. What you're asking is a question about "simultaneous diophantine approximation", q.v.
– Gerry Myerson
Nov 25 '18 at 11:34
@Gerry Myerson: Thank you, I did try and realized that as well, but wanted to come back in case I'm missing something. I will read about what you mentioned.
– RadekC
Nov 25 '18 at 12:15
|
show 2 more comments
I'm not a mathematician, so sorry for a confusing title. Let me explain.
For example, I'm shown a pie chart and it is split to 50% and 50%.
So logically, the smallest possible sample to achieve that would be 2. 1 and 1 = 50% and 50%.
What about if I'm given a pie chart with 70%, 15.87% and 14.13%.
How would I find out the smallest possible sample size, for which I could achieve these numbers?
So if someone shows me this pie chart without telling me the sample size, I can find out if their sample size was large enough (let's say it's only possible to achieve such a "precision" by dividing numbers above 500)
I mean naturally, to achieve the numbers I mentioned above, the sample size cannot be small, as you wouldn't achieve such a split with let's say a sample size of 5. The numbers are too "weird" for that (again, sorry for the non-scientific description...)
statistics percentages
asked Nov 25 '18 at 10:28
RadekC
1
I'm not a mathematician, so sorry for a confusing title. Let me explain.
For example, I'm shown a pie chart and it is split to 50% and 50%.
So logically, the smallest possible sample to achieve that would be 2. 1 and 1 = 50% and 50%.
What about if I'm given a pie chart with 70%, 15.87% and 14.13%.
How would I find out the smallest possible sample size, for which I could achieve these numbers?
So if someone shows me this pie chart without telling me the sample size, I can find out if their sample size was large enough (let's say it's only possible to achieve such a "precision" by dividing numbers above 500)
I mean naturally, to achieve the numbers I mentioned above, the sample size cannot be small, as you wouldn't achieve such a split with let's say a sample size of 5. The numbers are too "weird" for that (again, sorry for the non-scientific description...)
statistics percentages
statistics percentages
asked Nov 25 '18 at 10:28
RadekC
1
asked Nov 25 '18 at 10:28
RadekC
1
asked Nov 25 '18 at 10:28
RadekC
1
asked Nov 25 '18 at 10:28
RadekC
1
asked Nov 25 '18 at 10:28
RadekC
1
1
1
Multiply the values by $100$ to get $7000$, $1587$, and $1413$. Simplify by looking for the greatest common factor and then add up the simplified values.
– KM101
Nov 25 '18 at 10:43
A small addition to @KM101 's comment: you should multiply a value for every part by 10 until you get only integers. So, in an example with 50 and 50, you don't have to multiply anything, while in case of having, say, 50, 33.333 and 16.667, you should mutiply every value by 1000. After that, as it's been said, all you need is to find the greatest common factor for all those values
– Andrei Rykhalski
Nov 25 '18 at 10:50
Thank you so much, that's it! So silly I didn't think of that!
– RadekC
Nov 25 '18 at 10:59
That method don't work. Applied to $50,33.333,16.667$, you get $50000, 33333, 16667$ which have no common factor other than one, so you decide the sample size is $100000$. But in fact the sample size is $6$, it's just that the numbers have been rounded to three decimals. What you're asking is a question about "simultaneous diophantine approximation", q.v.
– Gerry Myerson
Nov 25 '18 at 11:34
@Gerry Myerson: Thank you, I did try and realized that as well, but wanted to come back in case I'm missing something. I will read about what you mentioned.
– RadekC
Nov 25 '18 at 12:15
|
show 2 more comments
1
Multiply the values by $100$ to get $7000$, $1587$, and $1413$. Simplify by looking for the greatest common factor and then add up the simplified values.
– KM101
Nov 25 '18 at 10:43
A small addition to @KM101 's comment: you should multiply a value for every part by 10 until you get only integers. So, in an example with 50 and 50, you don't have to multiply anything, while in case of having, say, 50, 33.333 and 16.667, you should mutiply every value by 1000. After that, as it's been said, all you need is to find the greatest common factor for all those values
– Andrei Rykhalski
Nov 25 '18 at 10:50
Thank you so much, that's it! So silly I didn't think of that!
– RadekC
Nov 25 '18 at 10:59
That method don't work. Applied to $50,33.333,16.667$, you get $50000, 33333, 16667$ which have no common factor other than one, so you decide the sample size is $100000$. But in fact the sample size is $6$, it's just that the numbers have been rounded to three decimals. What you're asking is a question about "simultaneous diophantine approximation", q.v.
– Gerry Myerson
Nov 25 '18 at 11:34
@Gerry Myerson: Thank you, I did try and realized that as well, but wanted to come back in case I'm missing something. I will read about what you mentioned.
– RadekC
Nov 25 '18 at 12:15
1
1
Multiply the values by $100$ to get $7000$, $1587$, and $1413$. Simplify by looking for the greatest common factor and then add up the simplified values.
– KM101
Nov 25 '18 at 10:43
Multiply the values by $100$ to get $7000$, $1587$, and $1413$. Simplify by looking for the greatest common factor and then add up the simplified values.
– KM101
Nov 25 '18 at 10:43
A small addition to @KM101 's comment: you should multiply a value for every part by 10 until you get only integers. So, in an example with 50 and 50, you don't have to multiply anything, while in case of having, say, 50, 33.333 and 16.667, you should mutiply every value by 1000. After that, as it's been said, all you need is to find the greatest common factor for all those values
– Andrei Rykhalski
Nov 25 '18 at 10:50
A small addition to @KM101 's comment: you should multiply a value for every part by 10 until you get only integers. So, in an example with 50 and 50, you don't have to multiply anything, while in case of having, say, 50, 33.333 and 16.667, you should mutiply every value by 1000. After that, as it's been said, all you need is to find the greatest common factor for all those values
– Andrei Rykhalski
Nov 25 '18 at 10:50
Thank you so much, that's it! So silly I didn't think of that!
– RadekC
Nov 25 '18 at 10:59
Thank you so much, that's it! So silly I didn't think of that!
– RadekC
Nov 25 '18 at 10:59
That method don't work. Applied to $50,33.333,16.667$, you get $50000, 33333, 16667$ which have no common factor other than one, so you decide the sample size is $100000$. But in fact the sample size is $6$, it's just that the numbers have been rounded to three decimals. What you're asking is a question about "simultaneous diophantine approximation", q.v.
– Gerry Myerson
Nov 25 '18 at 11:34
That method don't work. Applied to $50,33.333,16.667$, you get $50000, 33333, 16667$ which have no common factor other than one, so you decide the sample size is $100000$. But in fact the sample size is $6$, it's just that the numbers have been rounded to three decimals. What you're asking is a question about "simultaneous diophantine approximation", q.v.
– Gerry Myerson
Nov 25 '18 at 11:34
@Gerry Myerson: Thank you, I did try and realized that as well, but wanted to come back in case I'm missing something. I will read about what you mentioned.
– RadekC
Nov 25 '18 at 12:15
@Gerry Myerson: Thank you, I did try and realized that as well, but wanted to come back in case I'm missing something. I will read about what you mentioned.
– RadekC
Nov 25 '18 at 12:15
|
show 2 more comments
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1
Multiply the values by $100$ to get $7000$, $1587$, and $1413$. Simplify by looking for the greatest common factor and then add up the simplified values.
– KM101
Nov 25 '18 at 10:43
A small addition to @KM101 's comment: you should multiply a value for every part by 10 until you get only integers. So, in an example with 50 and 50, you don't have to multiply anything, while in case of having, say, 50, 33.333 and 16.667, you should mutiply every value by 1000. After that, as it's been said, all you need is to find the greatest common factor for all those values
– Andrei Rykhalski
Nov 25 '18 at 10:50
Thank you so much, that's it! So silly I didn't think of that!
– RadekC
Nov 25 '18 at 10:59
That method don't work. Applied to $50,33.333,16.667$, you get $50000, 33333, 16667$ which have no common factor other than one, so you decide the sample size is $100000$. But in fact the sample size is $6$, it's just that the numbers have been rounded to three decimals. What you're asking is a question about "simultaneous diophantine approximation", q.v.
– Gerry Myerson
Nov 25 '18 at 11:34
@Gerry Myerson: Thank you, I did try and realized that as well, but wanted to come back in case I'm missing something. I will read about what you mentioned.
– RadekC
Nov 25 '18 at 12:15