Last week at the Chandoo.org Forums, Sunita, posed the question:
“Please help me to find out the sum of odd numbers in a range of 1-100 numbers
Like 1+3+5+7+ … 97+ 99
How it will find through an excel formula?”
I chipped in with two array formulas:
=SUM(2*ROW(OFFSET($A$1,,,100/2))-1) Ctrl Shift Enter
and
=SUM(ROW(1:100)*MOD(ROW(1:100),2)) Ctrl Shift Enter
Lets look at each of these in turn.
As usual at Formula Forensics you can download a Sample File here and follow along Download Sample File.
Formula 1: =SUM(2*ROW(OFFSET($A$1,,,100/2))-1)
The first formula we will examine is:
=SUM(2*ROW(OFFSET($A$1,,,100/2))-1) Ctrl Shift Enter
This formula works on the principle of making an array of the odd numbers between 1 and 100 and the adding them up.
We can make an array of the odd numbers from 1 to 100 by:
- First make an array of all numbers from 1 to 50
- Second double the array values
- Subtract 1.
- Add up the values
1. Make an Array from 1 to 50
The formula ROW(OFFSET($A$1,,,100/2)) can be used to make an array of the numbers from 1 to 50
In a spare cell, D4, type =ROW(OFFSET($A$1,,,100/2)) then press F9 not enter
Excel will respond with an array: ={1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;27;28;29;30;31;32;33;34;35;36;37;38;39;40;41;42;43;44;45;46;47;48;49;50}
How does this work?
Offset($A$1,,,100/2) sets up a Range from A1 with no Row or Column offset, but with a height of 100/2 = 50.
In a spare cell, D6, type =OFFSET($A$1,,,100/2) then press F9 not enter
Excel will respond with an array: ={0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0}
We can see that the array contains 50 Zero’s (You can count them to check).
True.
But it is 50 Rows of Zero’s. The ;’s in the array separate Rows.
So the expanded formula: =ROW(OFFSET($A$1,,,100/2))
Returns the Rows of the Array Elements, not the Array Values.
2. Double the Values
The formula 2*ROW(OFFSET($A$1,,,100/2)) is used to double the array values
In a spare cell, D8, type =2*ROW(OFFSET($A$1,,,100/2)) then press F9 not enter
Excel will respond with an array: ={2;4;6;8;10;12;14;16;18;20;22;24;26;28;30;32;34;36;38;40;42;44;46;48;50;52;54;56;58;60;62;64;66;68;70;72;74;76;78;80;82;84;86;88;90;92;94;96;98;100}
3. Subtract 1
The formula 2*ROW(OFFSET($A$1,,,100/2)) -1 is used to subtract a value of a from the array values
In a spare cell, D10, type =2*ROW(OFFSET($A$1,,,100/2)) -1 then press F9 not enter
Excel will respond with an array: ={1;3;5;7;9;11;13;15;17;19;21;23;25;27;29;31;33;35;37;39;41;43;45;47;49;51;53;55;57;59;61;63;65;67;69;71;73;75;77;79;81;83;85;87;89;91;93;95;97;99}
4. Add up the Values
The formula =Sum(2*ROW(OFFSET($A$1,,,100/2)) -1) is used to add up the array values
In a spare cell, D12, type =Sum(2*ROW(OFFSET($A$1,,,100/2)) -1) then press F9 not enter
Excel will respond with a value of = 2500, The Answer.
Formula 2: =SUM(ROW(1:100)*MOD(ROW(1:100),2))
The second formula we will examine is:
=SUM(ROW(1:100)*MOD(ROW(1:100),2)) Ctrl Shift Enter
This formula works by constructing an array of values between 1 and 100 and then multiplying that Array by an Array of the Odd values between 1 and 100 and then adding up the resultant Array.
Lets start with: =SUM(ROW(1:100)*MOD(ROW(1:100),2))
Note that the Row(1:100) is used twice in the formula.
In a spare cell: D17 type: =Row(1:100) then press F9 not enter
Excel will respond with an array: ={1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;27;28;29;30;31;32;33;34;35;36;37;38;39;40;41;42;43;44;45;46;47;48;49;50;51;52;53;54;55;56;57;58;59;60;61;62;63;64;65;66;67;68;69;70;71;72;73;74;75;76;77;78;79;80;81;82;83;84;85;86;87;88;89;90;91;92;93;94;95;96;97;98;99;100}
An array of the values from 1 to 100.
Next we will look at the Mod section =SUM(ROW(1:100)*MOD(ROW(1:100),2))
In a spare cell: D19 type: =Mod(Row(1:100),2) then press F9 not enter
Excel will respond with an array: ={1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0;1;0}
Mod returns the remainder after dividing the first parameter by the second
Eg: Mod(5,2)=1 5 divided by 2 = 2 Remainder 1.
So in our example Mod( Array, 2 ) returns the value 1 for the Odd Values and 0 for the Even values.
Next we multiply the 2 arrays together: =SUM(ROW(1:100)*MOD(ROW(1:100),2))
This is the same as:
={1;2;3;4;5; … ;97;98;99;100} * {1;0;1;0;1; … ;1;0;1;0}
In a spare cell: D21 type: =ROW(1:100)*MOD(ROW(1:100),2) then press F9 not enter
Excel will respond with an array: ={1;0;3;0;5;0;7;0;9;0;11;0;13;0;15;0;17;0;19;0;21;0;23;0;25;0;27;0;29;0;31;0;33;0;35;0;37;0;39;0;41;0;43;0;45;0;47;0;49;0;51;0;53;0;55;0;57;0;59;0;61;0;63;0;65;0;67;0;69;0;71;0;73;0;75;0;77;0;79;0;81;0;83;0;85;0;87;0;89;0;91;0;93;0;95;0;97;0;99;0}
Finally we can add up the array values: =SUM(ROW(1:100)*MOD(ROW(1:100),2))
In a spare cell: D23 type: =SUM(ROW(1:100)*MOD(ROW(1:100),2)) then press F9 not enter
Excel will respond with a value of = 2500, The Answer.
Variation 1:
In the above formula =SUM(ROW(1:100)*MOD(ROW(1:100),2)) we described a method of evaluating Array values as either Odd or Even using the Mod function.
Excel has a built in function for determining if a Value is Odd and that is Isodd()
We can modify the above equation to use Isodd() as follows
=SUM(ROW(1:100)*ISODD(ROW(1:100)))
You can check it in cell D28.
What if I want to Sum the Even numbers?
We can use the variation described above to quickly add up the even numbers between 1 and 100
=SUM(ROW(1:100)*ISEVEN(ROW(1:100)))
In a spare cell: D21 type: =SUM(ROW(1:100)*ISEVEN(ROW(1:100))) then press F9 not enter
Excel will respond with a value of = 2550, The Answer.
How Else Can You Solve Sunita’s Problem?
Can you solve Sunita’s problem another way?
Let us know in the comments below:
Download
You can download a copy of the above file and follow along, Download Here.
Formula Forensics “The Series”
This is the 22nd post in the Formula Forensics series.
You can learn more about how to pull Excel Formulas apart in the following posts
Formula Forensics Needs Your Help
I need more ideas for future Formula Forensics posts and so I need your help.
If you have a neat formula that you would like to share and explain, try putting pen to paper and draft up a Post like above or;
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24 Responses
I’d suggest simply using the subtotal function and filtering the data using the Win/Loss column. You get the same results and the formula is more comprehensible.
@John
That is one option.
There are times however when you want to see the whole data table or a filtered subset and still want to produce summary reports against an unfiltered field.
Is there a particular reason why you are using a comma and the unary (–) operator for the second array in the SUMPRODUCT formula? It seems to work the same if you were to string the arrays together using the asterisk (*). The advantage is that SUMPRODUCT treats the entire string of arrays as a single array.
@Mathew
Your correct, There is no difference.
I thought it may have been easier to explain this method.
Is there a way to do this on a large set of data? As in ~100,000 rows? When I try I get an error because the formula becomes too long. It says the max length of a formula is 8,192 characters. Excel 2010.
How do I incorporate a specific text within a cell for the second array. For instance, – -(C7:C13=”Apple”)
when I chose a specific text the formula does not work.
@RB
I am not sure what is the issue as if I use the sample data in the post the following work fine
Count:
=SUMPRODUCT(SUBTOTAL(3,OFFSET(C7:C13,ROW(C7:C13)-MIN(ROW(C7:C13)),,1)), –(C7:C13=”L”))
Sum:
=SUMPRODUCT(SUBTOTAL(3,OFFSET(C7:C13,ROW(C7:C13)-MIN(ROW(C7:C13)),,1)),(C7:C13=”L”)*(D7:D13))
You may want to check that there are no leading or trailing spaces in your list of Apples
I should have given a better explanation. Heres my situation. I have a column with cells filled with names like Column 1, Column 2, Pier 1, Pier 2, etc. If the cell just contained Pier and searched for that it works. But because it has other characters in the cell its not recognizing the pier. So how can I extract specific characters of a string of text in this formula?
Hopefully this was a better explanation
Hello-
This formula works pretty well for me except that it slow down excel and prevents some of my macros from working. I was wondering if there was a way to program this in VBA so that excel isn’t always trying to recalculate it. I would like to use a push of a button to get it to run then paste in a cell.
Thanks!
I am trying to sum filtered data in a column, but would want to ignore the negative values in the column. How to go about doing this?
@Akshay
Why not just add a filter to that column to only show the values greater than zero?
The negative values are required for reporting purposes, but their effect on the total is distorting the required output. Please advise.
@Akshay
I’d suggest making a post in the Chandoo.org Forums
http://forum.chandoo.org/
Attach a sample file to simplify the task
I have this working for counting and summing, however, I have a list and for the second array, I need a criteria. That is, I’m looking for b13:b200=”01.??.??” or =left((a1,2) or something like that. These types of criteria matches do not appear to work as I get a blank as a result.
Thanks!
@Bob
As your formula b13:b200=”01.??.??” looks like you are trying to check the first day of the month of the range
What about trying Day(B13:B200)=1
Hai Experts,
i understood this formula well and working fine in MS Excel 2013
but when the same am trying to place in google Spreadsheet it shows error as
“SUMPRODUCT has mismatched range sizes. Expected row count: 1. column count: 1. Actual row count: 2014, column count: 1.” and as a result #VALUE! Appears in cell.
Can anyone please help me how would i get it done in Google Spread sheet
or is there any other formula as a substitute for this.
Thank you very much.
thanks for providing this.. but why does excel keeps on prompting Circular referencing in cell D3?
@Vivek
I don’t know
I just downloaded the file and it is working fine and not showing that error
Goto the Formulas, Calculation Options Tab and check that Calculation is set to Automatic
What version of Excel and Windows are you using ?
I know that this forum is for MS Excel, but I am trying to help someone who is working in Google Sheets. The below formula works in Excel but Google Sheets returns:
“SUMPRODUCT has mismatched range sizes. Expected row count: 1. column count: 1. Actual row count: 39000, column count: 1.” and as a result #VALUE! Appears in cell.
This is the same problem asked by Srichirin above. Does anyone know if there is a formula for Google Sheets that will replicate what MS Excel does?
=SUMPRODUCT(SUBTOTAL(3,OFFSET($C$6:$C$39500,ROW($C$6:$C$39500)-MIN(ROW($C$6:$C$39500)),,1)),- -($C$6:$C$39500=H1),($D$6:$D$39500))
Trying to find a SUMPRODUCT formula that counts the word Closed by date for the last 7 days in a filtered list.
=COUNTIF(M:M,”>”&TODAY()-7) works ok for unfiltered count Column M contains Closure dates (blank if open) and Column L is Status Open or Closed
@ Terry
Please ask the question at the Chandoo.org Forums
https://chandoo.org/forum/
Please attach a sample file to ensure a quicker more accurate answer
I used this formula and worked like a charm! But, now I’ve been requested to use it but adding not one but two criteria in the same formula. For instance the sum I was doing added negative and positive numbers. I’ve been asked to use the exact same formula but adding that only positive numbers were considered… any idea on how to do this?
How exactly do you do sum filtered cells when two criteria are need not just one?
Thank you so much brother literally I have been struggling since morning to get the sum of the filtered category, however, after reading your blog attentively i got my solution, so thanks a lot once again.