Re-post the question

Does anyone have any idea on how to determine the values under following
conditions?

Given a list of numbers sorted by ascending order from top to bottom under
column A, I would like to determine the minimum difference on the range
within this list covering 50% of total numbers, and return the smallest
number within the range in cell B1 and the largest number within the range in
cell B2.

For example, if the list contains 10 numbers, then I need to select 5 numbers
covering the minimum range, such as following example with 10 numbers, and I
need to select 50% of 10 = 5 numbers covering minimum ranges.

1,3,21,40,41,42,43,44,88,99

In this case, I should select 40,41,42,43,44
41 returns in cell B1
44 returns in cell B2

Does anyone have any suggestions?
Thank you in advance
Eric

By 50% I have interpretted that as 50% in the middle of the range i.e ignore
top/bottom (lowest/highest) 25%, based on your example.

With data in column A starting row 1:

B1:
=MIN(OFFSET($A$1,INT(COUNTA(A:A)/4)+1,0,INT(COUNTA(A:A)/2)))

B2:
=MAX(OFFSET($A$1,INT(COUNTA(A:A)/4)+1,0,INT(COUNTA(A:A)/2)))

You might want to adjust for list of even/odd number length.

B1=40 in your example, not 41

HTH

"Eric" wrote:

Re-post the question

Does anyone have any idea on how to determine the values under following
conditions?

Given a list of numbers sorted by ascending order from top to bottom under
column A, I would like to determine the minimum difference on the range
within this list covering 50% of total numbers, and return the smallest
number within the range in cell B1 and the largest number within the range in
cell B2.

For example, if the list contains 10 numbers, then I need to select 5 numbers
covering the minimum range, such as following example with 10 numbers, and I
need to select 50% of 10 = 5 numbers covering minimum ranges.

1,3,21,40,41,42,43,44,88,99

In this case, I should select 40,41,42,43,44
41 returns in cell B1
44 returns in cell B2

Does anyone have any suggestions?
Thank you in advance
Eric

On Fri, 23 Mar 2007 17:18:00 -0700, Eric
wrote:

Re-post the question

Does anyone have any idea on how to determine the values under following
conditions?

Given a list of numbers sorted by ascending order from top to bottom under
column A, I would like to determine the minimum difference on the range
within this list covering 50% of total numbers, and return the smallest
number within the range in cell B1 and the largest number within the range in
cell B2.

For example, if the list contains 10 numbers, then I need to select 5 numbers
covering the minimum range, such as following example with 10 numbers, and I
need to select 50% of 10 = 5 numbers covering minimum ranges.

1,3,21,40,41,42,43,44,88,99

In this case, I should select 40,41,42,43,44
41 returns in cell B1
44 returns in cell B2

Does anyone have any suggestions?
Thank you in advance
Eric


I assume that you want cell B1 to contain 40 rather than 41.

In the below I have generalized the problem to have any number of
numbers (but nothing else) in the column A.
If you always have 10 numbers you can replace COUNT(A:A) with 10 and
A:A with A1:A10 everywhere.

Introduce a help column, C, where you put the following in cell C1
and copy it down to cell Cn where n = 6 in the special case and
COUNT(A:A)/2+1 in the general case.

=INDEX(A:A;ROW()+COUNT(A:A)/2-1)-A1

In cell B1 put the following:
=INDEX(A:A;MATCH(SMALL(OFFSET(C1;0;0;COUNT(A:A)/2+1;1);OFFSET(C1;0;0;COUNT(A:A)/2+1);FALSE))

In cell B2 put the following:
=INDEX(A:A;MATCH(SMALL(OFFSET(C1;0;0;COUNT(A:A)/2+1;1);OFFSET(C1;0;0;COUNT(A:A)/2+1);FALSE)+COUNT(A:A)/2-1)

Hope this helps

larske

On Sat, 24 Mar 2007 00:20:03 -0700, Toppers
wrote:

By 50% I have interpretted that as 50% in the middle of the range i.e ignore
top/bottom (lowest/highest) 25%, based on your example.


This is not how I interprete the problem:

"minimum difference on the range within this list covering 50% of
total numbers"

My interpretation is that the range can be anywhere in the list.
Maybe the example could have been better choosen.

The following 10 numbers

10,20,30,40,50,55,60,65,70,90

should give 50 and 70 in B1 and B2 respectively if you ask me.
(Not 40 and 65)

larske

Hello,

That's what I think, too.

Select B1:B2 and array-enter
=TRANSPOSE(minmaxdensity50(A1:A10))

The UDF minmaxdensity50 has be inserted into a module (press ALT +
F11, insert module, then copy text shown below)

Regards,
Bernd


Function minmaxdensity50(r As Range) As Variant
Dim i As Long, j As Long, k As Long
Dim mi As Double, t As Double
Dim vR(0 To 1) As Variant
j = Int((r.Count - 2) / 2)
mi = Application.WorksheetFunction.Max(r) - _
Application.WorksheetFunction.Min(r)
For i = 1 To r.Count - j
t = r.Value2(i + j, 1) - r.Value2(i, 1)
If t < mi Then
mi = t
vR(0) = r.Value2(i, 1)
vR(1) = r.Value2(i + j, 1)
End If
Next i
minmaxdensity50 = vR
End Function

Thank everyone very much for suggestions
That is correct, I miss type the number, the cell B1 should be contained 40
rather than 41.
I am very appreciated everyone's helps
Thank everyone very much
Eric


"Lars-Ã…ke Aspelin" wrote:

On Fri, 23 Mar 2007 17:18:00 -0700, Eric
wrote:

Re-post the question

Does anyone have any idea on how to determine the values under following
conditions?

Given a list of numbers sorted by ascending order from top to bottom under
column A, I would like to determine the minimum difference on the range
within this list covering 50% of total numbers, and return the smallest
number within the range in cell B1 and the largest number within the range in
cell B2.

For example, if the list contains 10 numbers, then I need to select 5 numbers
covering the minimum range, such as following example with 10 numbers, and I
need to select 50% of 10 = 5 numbers covering minimum ranges.

1,3,21,40,41,42,43,44,88,99

In this case, I should select 40,41,42,43,44
41 returns in cell B1
44 returns in cell B2

Does anyone have any suggestions?
Thank you in advance
Eric


I assume that you want cell B1 to contain 40 rather than 41.

In the below I have generalized the problem to have any number of
numbers (but nothing else) in the column A.
If you always have 10 numbers you can replace COUNT(A:A) with 10 and
A:A with A1:A10 everywhere.

Introduce a help column, C, where you put the following in cell C1
and copy it down to cell Cn where n = 6 in the special case and
COUNT(A:A)/2+1 in the general case.

=INDEX(A:A;ROW()+COUNT(A:A)/2-1)-A1

In cell B1 put the following:
=INDEX(A:A;MATCH(SMALL(OFFSET(C1;0;0;COUNT(A:A)/2+1;1);OFFSET(C1;0;0;COUNT(A:A)/2+1);FALSE))

In cell B2 put the following:
=INDEX(A:A;MATCH(SMALL(OFFSET(C1;0;0;COUNT(A:A)/2+1;1);OFFSET(C1;0;0;COUNT(A:A)/2+1);FALSE)+COUNT(A:A)/2-1)

Hope this helps

larske

Hi Toppers:
I find a bug on your code, could you please give me any suggestion on how
to fix it?
If the list of numbers is 1 3 6 7 8 9 10 44 88 99
=MIN(OFFSET(A$1,INT(COUNT(A:A)/4)+1,0,INT(COUNT(A:A)/2))) 7
but the minimum should return 6
=MAX(OFFSET(A$1,INT(COUNT(A:A)/4)+1,0,INT(COUNT(A:A)/2))) 44
but the maximum should return 10
Does you have any suggestions?
I look forward to your reply
Thank you
Eric

Hi Bernd:
Could you please tell me how to locate this function under excel -
minmaxdensity50?
Thank you very much
Eric

"Bernd" wrote:

Hello,

That's what I think, too.

Select B1:B2 and array-enter
=TRANSPOSE(minmaxdensity50(A1:A10))

The UDF minmaxdensity50 has be inserted into a module (press ALT +
F11, insert module, then copy text shown below)

Regards,
Bernd


Function minmaxdensity50(r As Range) As Variant
Dim i As Long, j As Long, k As Long
Dim mi As Double, t As Double
Dim vR(0 To 1) As Variant
j = Int((r.Count - 2) / 2)
mi = Application.WorksheetFunction.Max(r) - _
Application.WorksheetFunction.Min(r)
For i = 1 To r.Count - j
t = r.Value2(i + j, 1) - r.Value2(i, 1)
If t < mi Then
mi = t
vR(0) = r.Value2(i, 1)
vR(1) = r.Value2(i + j, 1)
End If
Next i
minmaxdensity50 = vR
End Function