Percentiles (still hurting my brain)

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You wouldn't belive such a simple concept could cause so much trouble!

I've implemented Michael's algorithm in frequencies.q whcih we can run
with if we so desire.  If however, we want the SPSS one, then I'm all
at sea. =20

Let's run the data (1 2 3 4 5)  through  it, searching for the 50th
percentile:



     _SPSS Statistical Algorithms_ says, roughly:

W in this case is 5.    =20

     The p'th percentile:
    =20
     Find the first score interval (x2) containing more than tp cases.

Well further down it says that tp=3D(W+1)*p/W so tp=3D6*50/5 =3D 60
So the first problem is that there is no score with more than 60
cases.  So I assume that either Ben, or the typsetter of the book made
a mistake, and should have typed tp=3D(W+1)*p/100 in which case
tp =3D 6*50/100 =3D 3.

Thus x2 =3D 4 and x1 =3D 3

Now cc1 =3D 1+2+3 / 1+2+3+4+5 =3D 10/15 =3D 2/3
and therefore cp1 =3D 200/3

so tp - cp1 =3D 3 - 200/3  which doesn't satisfy the condition=20
tp-cp1 >=3D 100/W

So that answer is the 2nd case, viz:=20

1 - ((W+1)p/100 - cc1) x1 + ((W+1)p/100 - cc1)x2

which can be simplified to=20

1 + ((W+1)p/100 - cc1)( x2 - x1)

which in our case is


1 + (6 50/100 - 2/3)(4-3)

1 + ( 3 - 2/3)(1)

1 + ( 7/3)

10/3 =3D 3.333

which is a very poor value of the median of 1 2 3 4 5



No matter how many times I look at it, the algorithm that Ben posted
makes no sense to me.


Frustrated!

J'            =20

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