Data distribution
LOUiS
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I am having trouble recalling the exact rules for quintiles especially.
The problem is I don't understand a few key points about the division
of data into ranks.
Here is a sample from an answer booklet from a June review package:
(49, 54, 57, 58, 58) (60, 61, 61, 63, 66) (69, 70, 71, 75, 79, 79) (82,
85, 86, 87, 88) (91, 91, 93, 94, 99)
Where parentheses denote the beginnings and ends of quintile ranks.
If you could, please, tell me the step by step instructions for
determining quintile ranks, I have looked far and wide (on-line, at
least) for information on the method taught in Quebec.
Some questions that might help to clarify things: With Quartiles: If
Q1, 2 or 3 fall on a data entry, is it inclusive or exclusive to one of
the quartiles it defines? If inclusive, then to which quartile? With
Quintiles: Are quintile ranks defined by specific numbers, like
quartiles, or are they defined by grouping data together (As seems to
be the case in theexample.)? If the groups cannot be equal, because the
number of data entries is not divisible by 5, how does one decide how
to divide them?
Thank you for any time spent in my aid.
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And here is my answer.
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The rules for statistics can be a little confusing, especially since
they are not well defined anywhere except by the teacher teaching the
course.
Quartiles are specific numbers (Q1, Q2, Q3). They are read from
smallest to largest number (i.e. Q1 is smaller than Q2, which is
smaller than Q3) Q2 is your median (middle most number). If there isn't
one, find the average of the two middle most numbers. Q1 is the middle
most number between your Minimum and you Q2. Again, if there isn't one,
find the average of the two middle most numbers. Same with Q3 (between
Q2 and Maximum). Quintiles are groups of numbers (R1, R2, R3, R4, R5).
They are read from largest to smallest (i.e. the numbers in R1 are
larger than the numbers in R2, etc.) To divide up the numbers into
Quintiles, divide the total number by 5. This will give you an
approximate number of data per quintile (i.e. 26 divided by 5 is 5.2,
that means some groups will have 5 and some will have 6). These numbers
are more like guidelines, and are not set in stone. To separate the
groups, use the following rules:
1- Try not to separate the numbers that are the same (i.e. 69 ], [ 70,
70)
2- Try not to separate numbers that are close to each other in value
(i.e. 68, 69, 70 ], [ 75, 76)
Unless you break one of these rules, there is no wrong way to
distribute the groups. Quintiles are flexible, in a way. As for the
example you supplied, to create a box-and-whisker plot:
49 is you minimum and 99 is you maximum.
There are 26 values, so your Q2 is the average of 71 and 75... 73.
Now, there are 13 values between your min and Q2, and between Q2 and
max.
So, the 7th number is your Q1... 61.
And your Q3 is 87.
Your box-and-whisker plot would look like this:
|-----|=====|=====|-----|
49 61 71 87 99
Min Q1 Q2 Q3 Max
The numbers between 49, 61, 71, 87, 99 do not belong to any quartiles,
they are just data. Quartiles are just medians. Quintiles define groups
and are not one number, but many. Q2 cannot be 71 to 87, for example.
Q2 is 71 R2 cannot be 82, for example. R2 is 82 to 88. Your quintile
ranks would be divided like this:
[49, 54, 57,
58,58][60,61,61,63,66][69,70,71,75,79,79][82,85,86,87,88][91,91,93,94,99]
And they would be labelled as follows:
[R5][R4][R3][R2][R1]
In the first division:[57, 58, 58 (gap) 60, 61, 61].
In the second:[61, 63, 66 (gap) 69, 70, 71]
Third:[75, 79, 79 (gap) 82, 85, 86]
Fourth:[86, 87, 88 (gap) 91, 91, 93]
It takes a bit of practice, but it becomes easier and easier to tell
where the gaps are in time.
I hope this has helped to clarify some things.
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