Formula Forensics 016. Suzannes DJIA Average

Formula Forensics 016. Suzannes DJIA Average:
Last week Suzanne asked a question over at the Excel Hero Academy.
“I was trying to calculate the average DJIA # by month. I had the data by day so tried various combos (none of which worked (:-”
Suzanne’s Formula: =AVERAGE($A$2:$A$20=31/3/2010, B2:B20)
So today we will pull Suzanne’s Formula apart to see what’s inside and why it didn’t work.
And then we’ll go on to recommend a solution.

Suzanne’s Formula

As usual we will work through this formula using a sample file for you to follow along. Download Here.
Suzanne’s formula uses a simple Excel Average( ) function.
=AVERAGE($A$2:$A$20=31/3/2010, B2:B20)
The Average Function has the syntax

So Average will sum up the numbers in the function or supplied Ranges and then divide by the number of entries or cells in the range
If we look at Suzanne’s formula =AVERAGE($A$2:$A$20=31/3/2010, B2:B20)
We can see that it has two ranges
=AVERAGE($A$2:$A$20=31/3/2010, B2:B20)

Range 1: $A$2:$A$20=31/3/2010
Range 2: B2:B20

Lets look at the first range
Range 1: $A$2:$A$20=31/3/2010
In a blank cell say E12 enter =$A$2:$A$20=31/3/2010 then press F9 instead of Enter
Excel will return ={FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE}
This is telling us a few things:
Firstly that none of the cells in the range match the date 31/3/2010
But we can see that the first 6 items all match.
So maybe it is the format of the date?
In a 2^nd blank cell say E13 enter =$A$2:$A$20=”31/3/2010” then press F9 instead of Enter
Excel will return ={FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE}
Once again Excel is not finding any matches.
In a 3^rd blank cell say cell E14 enter =$A$2:$A$20=Date(2010,3,31) then press F9 instead of Enter
Excel will return ={TRUE; TRUE; TRUE; TRUE; TRUE; TRUE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE}
Bingo, We now have 6 matches. Suzanne was using a bad syntax for matching the dates.

Now lets look at the second range
Range 2: B2:B20
In a blank cell say E16 enter =B2:B20 then press F9 instead of Enter
Excel will return = {10552.52; 10564.38; 10567.33; 10611.84; 10624.69; 10642.15; 10685.98; 10733.67; 10779.17; 10741.98; 10785.89; 10888.83; 10836.15; 10841.21; 10850.36; 10895.86; 10907.42; 10856.63; 10927.07}
It is a list of all the numbers between B2 and B20, they have all been included.
If we return to the Suzanne’s original formula
=AVERAGE($A$2:$A$20=31/3/2010, B2:B20)
We can now see that the two ranges will translate to
=AVERAGE({FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE},{10552.52; 10564.38; 10567.33; 10611.84; 10624.69; 10642.15; 10685.98; 10733.67; 10779.17; 10741.98; 10785.89; 10888.83; 10836.15; 10841.21; 10850.36; 10895.86; 10907.42; 10856.63; 10927.07})
So in E18 now enter =AVERAGE({FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE},{10552.52; 10564.38; 10567.33; 10611.84; 10624.69; 10642.15; 10685.98; 10733.67; 10779.17; 10741.98; 10785.89; 10888.83; 10836.15; 10841.21; 10850.36; 10895.86; 10907.42; 10856.63; 10927.07})
Excel returns 10752.27, which is the incorrect answer that we also see in Suzanne’s formula in E4
Excel, true to form has done exactly what we asked it to do, except that we have asked it to do the wrong thing.

So How Do We Average the DJIA Values

How do we average the DJIA values where the date is equal to 31/3/2010.
We saw that in the 3rd Blank cell E14 that when we entered =$A$2:$A$20=Date(2010,3,31), Excel responded with an array of True/False values, where the dates matched our value.
We can use a small modification to this to just extract the exact dates and ignore the rest.
If we simply use this formula in conjunction with an If( ) function
IF($A$2:$A$20=DATE(2010,3,31), $B$2:$B$20)
In the If function if the cells in A2:A20 match the Date of 31/3/2010 then Excel will return the True value or the corresponding value from B2:B20
To test this in a Blank cell say E20 enter =IF($A$2:$A$20=DATE(2010,3,31),$B$2:$B$20) press F9
Excel responds with an array ={10552.52; 10564.38; 10567.33; 10611.84; 10624.69; 10642.15; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE}
Excel has returned an array of the first 6 values from B2:B20 which correspond to the 6 matching cells from A2:A20 and the returned False for the remaining cells from B8:B20
If we include this array in an Average Function we should be home.
In Cell E6 enter the formula =AVERAGE(IF($A$2:$A$20=DATE(2010,3,31),$B$2:$B$20)) Press Ctrl Shift Enter instead of Enter
Excel responds with 10,593.8183 matching our manual calculations in cell E2.

Why Didn’t we put a False Value in the If statement ?

In Cell E22 enter the formula =IF($A$2:$A$20=DATE(2010,3,31),$B$2:$B$20,0) Press Ctrl Shift Enter instead of Enter
Excel responds with an array ={10552.52; 10564.38; 10567.33; 10611.84; 10624.69; 10642.15; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0}
This is the first 6 values from Column B matching our criteria and the 13 entries of 0 where it doesn’t match
If we sum these numbers up we get 63,562.91
If we divide 63,562.91 by 19 (the number of values) we get an average of 3,345.42
We can see that excel has included the 13, “0″ values in the average as numbers hence reducing the average, where it has ignored the 13 Falses in our previous formula to just average the 6 matching values.

An Alternative

I don’t know why Suzanne decided to write her own formula for this problem, as Colonel Shultz said “I know noooothing”.
I do know however that Excel has a dandy function which will solve this problem for Suzanne without using an Array Formula?
It’s called Averageifs( ). It is new to Excel 2007 and above.
Suzannes problem is simply solved with:
=AVERAGEIFS(B2:B20, A2:A20, DATE(2010,3,31))
Which says, Average column B2:B20 where Column A2:A20 = 31 March 2010
Benefits of Averageifs
The two benefits of using Averageifs( )
1. It isn’t array entered
2. It can have multiple other conditions added to it
Shortcoming of Averageifs
The main shortcoming of Averageifs( )
1. It is not available in Excel before 2007

Download

You can download a copy of the above file and follow along, Download Here.

Formula Forensics “The Series”

You can learn more about how to pull Excel Formulas apart in the following posts
Formula Forensic Series

Formula Forensics Needs Your Help

I urgently 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;
If you have a formula that you would like explained but don’t want to write a post also send it to Chandoo or Hui.

ps: Happy Birthday Jhuvy !

Happy Birthday Jhuvy !