Can someone explain, in detail, how I work this question out?
Find the mean of the following set of data (x) using the coding y = x+10/100
120 165 98 215 145 103 68 240

nousernametho
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 04102016 18:12

Kevin De Bruyne
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 04102016 18:15
(Original post by nousernametho)
Can someone explain, in detail, how I work this question out?
Find the mean of the following set of data (x) using the coding y = x+10/100
120 165 98 215 145 103 68 240
You can do it manually if you wish BUT...
If x was your set of values with mean 'a' and you divided each term by 100, what would the new mean be in terms of a? This will not get you the complete answer but will send you in the right direction and hopefully boost your understanding.Last edited by Kevin De Bruyne; 04102016 at 18:19. 
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 04102016 18:19
don't trust this 100% because we covered this for like 5 minutes in stats and then moved on so... sorry
linear coding is basically a way of using 'nicer' numbers when working out things such as mean and standard deviation.
To work out the mean, first add 10 and divide by 100 to each term as that is what the 'coding rule' is for this question. With the coded values of x, proceed to find the mean as normal, and then at the end reverse the coding for the mean.
Eg. If you got that your answer for the mean with coding was 4, then the mean without the coding is 4*100  10 = 390.Spoiler:ShowAlso, for standard deviation, you would multiply your final result by 100 but wouldn't add 10 because standard deviation is just the spread of the data, so adding 10 wouldn't change this spread.Last edited by surina16; 04102016 at 18:23. 
nousernametho
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 04102016 18:28
(Original post by SeanFM)
What is the urgency  test tomorrow?
You can do it manually if you wish BUT...
If x was your set of values with mean 'a' and you divided each term by 100, what would the new mean be in terms of a? This will not get you the complete answer but will send you in the right direction and hopefully boost your understanding.
I've done it now, thank you for your help! Let's just hope I've got it right. 
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 04102016 18:30
(Original post by surina16)
don't trust this 100% because we covered this for like 5 minutes in stats and then moved on so... sorry
linear coding is basically a way of using 'nicer' numbers when working out things such as mean and standard deviation.
To work out the mean, first add 10 and divide by 100 to each term as that is what the 'coding rule' is for this question. With the coded values of x, proceed to find the mean as normal, and then at the end reverse the coding for the mean.
Eg. If you got that your answer for the mean with coding was 4, then the mean without the coding is 4*100  10 = 390.Spoiler:ShowAlso, for standard deviation, you would multiply your final result by 100 but wouldn't add 10 because standard deviation is just the spread of the data, so adding 10 wouldn't change this spread. 
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 04102016 18:30
(Original post by nousernametho)
Haha, nah it's homework due in for tomorrow, but my teacher said: "You will need to do independent research on coding as I'm not telling you how to do it, so don't come asking me. Google it." ~ I Googled it and the majority of it didn't make sense...
I've done it now, thank you for your help! Let's just hope I've got it right.
What did you end up with? / how did you do it? Happy to check over your work if you post it here 
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 04102016 18:35
Here's what I did  thank you for helping!
(Original post by SeanFM)
If you have the Edexcel textbook it should be in there if you don't have the textbook.. then your school is silly.
What did you end up with? / how did you do it? Happy to check over your work if you post it here 
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 04102016 18:38
Let's say I had the set x, which contains 5,10,15,20,25. (The mean is 15, as you can see, the same as the median but that is a coincidence for this example).
If I had the coding y= x /5 , what is the new mean? And what do you notice about the old mean compared to the new mean, compared to the coding?Last edited by Kevin De Bruyne; 04102016 at 18:44. 
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 04102016 18:43
(Original post by SeanFM)
That may get you the write answer but it's not the intended method.
Let's say I had the set 5,10,15,20,25. (The mean is 15, as you can see, the same as the median but that is a coincidence for this example).
If I had the coding y= x /5 , what is the new mean? And what do you notice about the old mean compared to the new mean, compared to the coding? 
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 04102016 18:46
(Original post by nousernametho)
Wait, so do I not make, in this example, 5, 10, 15, 20 and 25 the x values and then sub. that into the equation to calculate the mean?
(the y values are 1,2,3,4,5 to save you time) 
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 04102016 18:51
(Original post by SeanFM)
Yes, that is what I want you to do for the purpose of this question and then see the link between the mean of x, the mean of y and the coding (y = x/5)
(the y values are 1,2,3,4,5 to save you time)
Comparing that mean to the original mean: it's smaller. Or have I gone wrong somewhere? 
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 04102016 18:57
(Original post by nousernametho)
So the new mean would be 3 (because 1+2+3+4+5=15, and then 15/5 = 3).
Comparing that mean to the original mean: it's smaller. Or have I gone wrong somewhere?
The old mean of 5,10,15,20,25 is 15 and the new mean when you apply y = x/5, is 3. It is no coincidence that 15/5 = 3...
This is because if you divide each term by a constant, then the mean will also be divided by that constant.
See that the mean of (5/5, 10/5, 15/5, 20/5, 25/5) is 1/5 * the mean of (5, 10, 15, 20, 25).. and in general, if you are multiplying a set x by a (in this case a is a fraction, 1/5) then the new mean is a * the mean of x.You can see this now as mean(x) = 15, a = 1/5 and mean(y) = 3 (the mean of x and y you calculated...) and so you know that this formula works.
With me so far? this is half of the challenge of working out the new mean of (x+10)/100, but it's not as simple as mean(x) / 100 because of the +10. But it's important for you to understand what happens when you have y = ax first.Last edited by Kevin De Bruyne; 04102016 at 18:59. 
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 04102016 19:12
(Original post by SeanFM)
Not quite what I mean by comparing, but I appreciate that the question is ambiguous unless you know what you're looking for.
The old mean of 5,10,15,20,25 is 15 and the new mean when you apply y = x/5, is 3. It is no coincidence that 15/5 = 3...
This is because if you divide each term by a constant, then the mean will also be divided by that constant.
See that the mean of (5/5, 10/5, 15/5, 20/5, 25/5) is 1/5 * the mean of (5, 10, 15, 20, 25).. and in general, if you are multiplying a set x by a (in this case a is a fraction, 1/5) then the new mean is a * the mean of x.You can see this now as mean(x) = 15, a = 1/5 and mean(y) = 3 (the mean of x and y you calculated...) and so you know that this formula works.
With me so far? this is half of the challenge of working out the new mean of (x+10)/100, but it's not as simple as mean(x) / 100 because of the +10. But it's important for you to understand what happens when you have y = ax first. 
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 04102016 19:14
(Original post by nousernametho)
Oh right, I think I see where you're coming from now, thank you so much for helping me!
And if you had a set with mean x, and added 5 to each term (i.e y = x +5) what is the new mean then? 
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 04102016 19:20
(Original post by SeanFM)
Right so if I had a set with mean 18 and coding y = x/6, what is the new mean?
And if you had a set with mean x, and added 5 to each term (i.e y = x +5) what is the new mean then?
I'm a bit confused with the bolded part, assuming that my first answer is right? Do I substitute x for numerical values (i.e. 1,2,3,4,5...?) 
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 04102016 19:23
(Original post by nousernametho)
So, the old mean is 18, and the new mean when you apply y=x/6 is y=18/6 which is 3. So the new mean is 3? Right so far?
I'm a bit confused with the bolded part, assuming that my first answer is right? Do I substitute x for numerical values (i.e. 1,2,3,4,5...?)
Sorry, I should have been more clear  the second part is a new set, can be anything.
If you had a set x containing 2,4,6,8,10 and added 5 to each set (i.e y = x +5) then what is the new mean, and so what is the link between the old mean, the new mean and the coding? (Same question as before so now you know what kind of answer you need) 
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 04102016 19:29
(Original post by SeanFM)
Correct, the new mean is 3 you can do that without knowing the actual points themselves, same with the +5.
Sorry, I should have been more clear  the second part is a new set, can be anything.
If you had a set x containing 2,4,6,8,10 and added 5 to each set (i.e y = x +5) then what is the new mean, and so what is the link between the old mean, the new mean and the coding? (Same question as before so now you know what kind of answer you need)
I'm really unsure about the link though. 
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 04102016 19:32
(Original post by nousernametho)
Okay, so if the set contains 2,4,6,8,10 then this makes the new set, when applying y=x+5: 7,9,11,13,15. If I calculate a mean from here I get: 55/5 = 11. Is that bit right?
I'm really unsure about the link though.
Okay, no worries.
Remember last time the coding was y = x/5, the old mean was 15 and the new mean was 3.. and the link was what x is being multiplied by (here it was multiplied by 1/5). When the set x is multiplied by a number a, the mean is multiplied by that number a as well.
Now you have the old mean being 6 and the new mean being 11.. and the code is y = x + 5.. so what is the link? 
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 04102016 21:28
(Original post by SeanFM)
Correct
Okay, no worries.
Remember last time the coding was y = x/5, the old mean was 15 and the new mean was 3.. and the link was what x is being multiplied by (here it was multiplied by 1/5). When the set x is multiplied by a number a, the mean is multiplied by that number a as well.
Now you have the old mean being 6 and the new mean being 11.. and the code is y = x + 5.. so what is the link?
Okay, so is the link something along the lines of, that, as x increases, the mean also increases? 
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 04102016 21:32
(Original post by nousernametho)
(Sorry for the late reply)
Okay, so is the link something along the lines of, that, as x increases, the mean also increases?
You might be overcomplicating this (though admittedly I could explain it better).. if you look back to the example where the mean was 9, you added 5 to everything and the new mean was 14...
(y=x+5).
What I am trying to show you here is that mean(y) = mean(x) + 5, and more generally, if y = x +a where a can be any positive or negative value, then mean(y) = mean (x) + a. Can you see the link now? It is similar to the link with the mean, just a different calculation (i.e before it was multiplying the set x, now you're adding..)Last edited by Kevin De Bruyne; 04102016 at 21:34.
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