ArrayFormula of Average on Infinite Truly Dynamic Range in Google Sheets

QUERY

level 1:

if all 5 cells in range C2:G have values:

=QUERY(QUERY(C2:G, "select (C+D+E+F+G)/5"), "offset 1", )

if not, then rows are skipped:

if empty cells are considered as zeros:

=INDEX(QUERY(QUERY({C2:G*1}, "select (Col1+Col2+Col3+Col4+Col5)/5"), "offset 1", ))

to remove zero values we use IFERROR(1/(1/...)) wrapping:

=INDEX(IFERROR(1/(1/QUERY(QUERY({C2:G*1}, 
 "select (Col1+Col2+Col3+Col4+Col5)/5"), "offset 1", ))))

to make Col references dynamic we can do:

=INDEX(IFERROR(1/(1/QUERY(QUERY({C2:G*1}, 
 "select "&
 "("&JOIN("+", "Col"&ROW(INDIRECT("1:"&COLUMNS(C:G))))&")/"&COLUMNS(C:G)), 
 "offset 1", ))))

level 2:

if empty cells are not considered as zeros and shouldn't be skipped:

=INDEX(TRANSPOSE(QUERY(TRANSPOSE(E2:I), 
 "select "&TEXTJOIN(",", 1, IF(A2:A="",,
 "avg(Col"&ROW(A2:A)-ROW(A2)+1&")")))),, 2)

note that this is column A dependant, so missing values in column A will offset the results

fun fact !! we can swap avg to max or min:

to free it from confinement of column A and make it work for any valid row:

=INDEX(IFERROR(1/(1/TRANSPOSE(QUERY(TRANSPOSE(
 IF(TRIM(TRANSPOSE(QUERY(TRANSPOSE(C2:G),,9^9)))="", C2:G*0, C2:G)), 
 "select "&TEXTJOIN(",", 1, 
 "avg(Col"&ROW(A2:A)-ROW(A2)+1&")"))))),, 2)

if present 0's in range shouldn't be averaged we can add a small IF statement:

=INDEX(IFERROR(1/(1/TRANSPOSE(QUERY(TRANSPOSE(
 IF(TRIM(TRANSPOSE(QUERY(TRANSPOSE(
 IF(C2:G>0, C2:G, )),,9^9)))="", C2:G*0, 
 IF(C2:G>0, C2:G, ))), 
 "select "&TEXTJOIN(",", 1, 
 "avg(Col"&ROW(A2:A)-ROW(A2)+1&")"))))),, 2)

here we used so-called "vertical query smash" which takes all values in a given range and concentrates it to one single column, where all cells per each row are joined with empty space as a byproduct:

=FLATTEN(QUERY(TRANSPOSE(C2:G),,9^9))

apart from this, there is also "horizontal query smash":

=QUERY(C2:G,,9^9)

and also "ultimate 360° double query smash" which puts all cells from range into one single cell:

=QUERY(FLATTEN(QUERY(TRANSPOSE(C2:G),,9^9)),,9^9)

and finally "the infamous negative 360° reverse double query smash" which prioritizes columns over rows:

=QUERY(FLATTEN(QUERY(C2:G,,9^9)),,9^9)

all query smash names are copyrighted of course

back to the topic... as mentioned above all cells per row in range are joined with empty space even those empty ones, so we got a situation where we getting double or multiple spaces between values. to fix this we use TRIM and introduce a simple IF statement to assign 0 values for empty rows in a given range eg. to counter the offset:

MMULT

level 3:

MMULT is a kind of heavy class formula that is able to perform addition, subtraction, multiplication, division even running total on arrays/matrixes... however, bigger the dataset = slower the formula calculation (because in MMULT even empty rows take time to perform + - × ÷ operation) ...unless we use truly dynamic range infinite in both directions...

to get the last row with values of a given range:

=INDEX(MAX(IF(TRIM(FLATTEN(QUERY(TRANSPOSE(
 INDIRECT("C2:"&ROWS(A:A))),,9^9)))="",,ROW(A2:A))))

to get the last column with values of a given range:

=INDEX(MAX(IF(TRIM(QUERY(INDIRECT("C2:"&ROWS(A:A)),,9^9))="",,COLUMN(C2:2))))

now we can construct it in a simple way:

=INDIRECT("C2:"&ADDRESS(9, 7))

which is the same as:

=INDEX(INDIRECT("C2:"&ADDRESS(MAX(IF(TRIM(FLATTEN(QUERY(TRANSPOSE(
 INDIRECT("C2:"&ROWS(A:A))),,9^9)))="",,ROW(A2:A))), 
 MAX(IF(TRIM(QUERY(INDIRECT("C2:"&ROWS(A:A)),,9^9))="",,COLUMN(C2:2))))))

or shorter alternative:

=INDEX(INDIRECT("C2:"&ADDRESS(
 MAX((INDIRECT("C2:"&ROWS(A:A))<>"")*ROW(A2:A)), 
 MAX((INDIRECT("C2:"&ROWS(A:A))<>"")*COLUMN(C2:2)))))

therefore simplified MMULT formula would be:

=ARRAYFORMULA(IFERROR(
 MMULT(N(   C2:G9),           ROW(INDIRECT("C1:C"&COLUMNS(C:G)))^0)/
 MMULT(N(IF(C2:G9<>"", 1, )), ROW(INDIRECT("C1:C"&COLUMNS(C:G)))^0)))

in case we want to exclude zero values from range, the formula would be:

=ARRAYFORMULA(IFERROR(
 MMULT(N(   C2:G9),         ROW(INDIRECT("C1:C"&COLUMNS(C:G)))^0)/
 MMULT(N(IF(C2:G9>0, 1, )), ROW(INDIRECT("C1:C"&COLUMNS(C:G)))^0)))

level 4:

putting together all above to make it infinitely dynamic and still restricted to valid dataset:

=INDEX(IFERROR(
 MMULT(N(   INDIRECT("C2:"&ADDRESS(
 MAX((INDIRECT("C2:"&ROWS(A:A))<>"")*ROW(A2:A)), 
 MAX((INDIRECT("C2:"&ROWS(A:A))<>"")*COLUMN(C2:2))))),           ROW(INDIRECT("C1:C"&
 MAX((INDIRECT("C2:"&ROWS(A:A))<>"")*COLUMN(C2:2))-(COLUMN(C2)-1)))^0)/
 MMULT(N(IF(INDIRECT("C2:"&ADDRESS(
 MAX((INDIRECT("C2:"&ROWS(A:A))<>"")*ROW(A2:A)), 
 MAX((INDIRECT("C2:"&ROWS(A:A))<>"")*COLUMN(C2:2))))<>"", 1, )), ROW(INDIRECT("C1:C"&
 MAX((INDIRECT("C2:"&ROWS(A:A))<>"")*COLUMN(C2:2))-(COLUMN(C2)-1)))^0)))

again, not including cells with zeros in range:

honorable mentions:

@Erik Tyler level:

the polar opposite of the previous formula would be to run the MMULT on

• total area of C2:? (all rows, all columns) instead of
• valid area C2:? (excluding empty rows and columns) which avoids mass-calculations of 0 × 0 = 0

including zeros:

=INDEX(IFERROR(
 MMULT(   INDIRECT("C2:"&ROWS(C:C))*1,         SEQUENCE(COLUMNS(C2:2))^0)/ 
 MMULT(IF(INDIRECT("C2:"&ROWS(C:C))<>"", 1)*1, SEQUENCE(COLUMNS(C2:2))^0)))

excluding zeros:

=INDEX(IFERROR(
 MMULT(   INDIRECT("C2:"&ROWS(C:C))*1,       SEQUENCE(COLUMNS(C2:2))^0)/ 
 MMULT(IF(INDIRECT("C2:"&ROWS(C:C))>0, 1)*1, SEQUENCE(COLUMNS(C2:2))^0)))

@kishkin level:

for a fixed range C2:G9 the MMULT average would be:

=INDEX(IFERROR(
 MMULT( C2:G9*1,    FLATTEN(COLUMN(C:G))^0)/ 
 MMULT((C2:G9>0)*1, FLATTEN(COLUMN(C:G))^0)))

=INDEX(IFNA(VLOOKUP(ROW(C2:C), 
 QUERY(SPLIT(FLATTEN(ROW(C2:C)&"×"&C2:J), "×"),
 "select Col1,avg(Col2)
  where Col2 is not null
  group by Col1"), 2, )))

@MattKing level:

=INDEX(QUERY(SPLIT(FLATTEN(ROW(C2:C)&"×"&OFFSET(C2,,,9^9, 9^9)), "×"),
 "select avg(Col2) 
  group by Col1  
  label avg(Col2)''"))

excluding zeros:

=INDEX(QUERY(SPLIT(FLATTEN(ROW(C2:C)&"×"&OFFSET(C2,,,9^9, 9^9)), "×"),
 "select avg(Col2)
  where Col2 <> 0 
  group by Col1  
  label avg(Col2)''"))

including empty cells:

=INDEX(IFERROR(1/(1/QUERY(SPLIT(FLATTEN(ROW(C2:C)&"×"&OFFSET(C2,,,9^9, 9^9)*1), "×"),
 "select avg(Col2)
  group by Col1  
  label avg(Col2)''"))))

You put a ton of time into this. I hope people appreciate it, more so that you did it for everyone else and not for yourself.

Looking at your final formulas, these should produce the same results (give data in C2:? as in your examples):

In B2 (include zeros):

=ArrayFormula(IFERROR(MMULT(INDIRECT("C2:"&ROWS(C:C))*1,SEQUENCE(COLUMNS(C1:1),1,1,0))/ MMULT(IF(INDIRECT("C2:"&ROWS(C:C))<>"",1,0),SEQUENCE(COLUMNS(C1:1),1,1,0))))

In B2 (exclude zeros):

=ArrayFormula(IFERROR(MMULT(INDIRECT("C2:"&ROWS(C:C))*1,SEQUENCE(COLUMNS(C1:1),1,1,0))/ MMULT(IF(INDIRECT("C2:"&ROWS(C:C))<>0,1,0),SEQUENCE(COLUMNS(C1:1),1,1,0))))

UPDATE: I've updated the formula from my original post. The ROW() should always come first so that missing values in the data don't throw off the split.

=ARRAYFORMULA(QUERY(SPLIT(FLATTEN(ROW(C2:C)&"|"&OFFSET(C2,,,9^9,9^9)),"|"),"select AVG(Col2) group by Col1 label AVG(Col2)''"))

Should work unless I'm misunderstanding the question.

No need for vlookups or mmults or filters or anything.

I will try to make a little addition to @player0's answer. And I will really appreciate any comments on optimizing this.

In case there is a lot of empty rows and columns inside the data range those might as well be excluded from MMULT.

Step 1 - Filter out empty rows

We've got a data range: from C2 down to the last row and right to the last column (which is J:J). I will use C2:K, see details below for explanation.

This formula will give us an array of row numbers where there is at least one non empty cell. Also it will have a 0 if there are empty rows, but it won't matter for searching in this array, or we will filter it out when it does matter:

=ARRAYFORMULA(
  UNIQUE(FLATTEN((C2:K <> "") * ROW(C2:K)))
)

So, to filter out empty rows from the data range we use FILTER which will check if a row is in our array from above and leave if be in that case:

=ARRAYFORMULA(
  FILTER(
    C2:K*1,
    MATCH(
      ROW(C2:K),
      UNIQUE(FLATTEN((C2:K <> "") * ROW(C2:K))),
      0
    )
  )
)

Step 2 - Filter out empty columns

To get an array of only non-empty column numbers we can use almost the same formula:

=ARRAYFORMULA(
  UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2))))
)

Why SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)) is used instead of COLUMN(C2:K) see details at the end.

To filter out empty columns we also use FILTER with MATCH condition to search for column numbers in our array:

=ARRAYFORMULA(
  FILTER(
    C2:K*1,
    MATCH(
      SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)),
      UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)))),
      0
    )
  )
)

And to filter out empty rows and empty columns we just use two FILTERs:

=ARRAYFORMULA(
  FILTER(
    FILTER(
      C2:K*1,
      MATCH(
        ROW(C2:K),
        UNIQUE(FLATTEN((C2:K <> "") * ROW(C2:K))),
        0
      )
    ),
    MATCH(
      SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)),
      UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)))),
      0
    )
  )
)

Original data range will internally become:

Step 3 - Do the MMULT

Now we can use MMULT with that data set to calculate average:

=ARRAYFORMULA(
  MMULT(
    FILTER(
      FILTER(
        C2:K*1,
        MATCH(
          ROW(C2:K),
          UNIQUE(FLATTEN((C2:K <> "") * ROW(C2:K))),
          0
        )
      ),
      MATCH(
        SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)),
        UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)))),
        0
      )
    ),
    SEQUENCE(
      ROWS(
        QUERY(
          UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)))),
          "WHERE Col1 <> 0"
        )
      ),
      1,
      1,
      0
    )
  ) /
  MMULT(
    FILTER(
      FILTER(
        (C2:K <> "")*1,
        MATCH(
          ROW(C2:K),
          UNIQUE(FLATTEN((C2:K <> "") * ROW(C2:K))),
          0
        )
      ),
      MATCH(
        SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)),
        UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)))),
        0
      )
    ),
    SEQUENCE(
      ROWS(
        QUERY(
          UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)))),
          "WHERE Col1 <> 0"
        )
      ),
      1,
      1,
      0
    )
  )
)

It is a bit off regarding original data rows.

Step 4 - Fill the AVERAGE column

To make averages consistent with the original data rows we can use VLOOKUP like this:

=ARRAYFORMULA(
  IFNA(VLOOKUP(
    SEQUENCE(MAX((C2:K <> "") * ROW(C2:K)) - 1, 1, ROW(C2)),
    {
      QUERY(UNIQUE(FLATTEN((C2:K <> "") * ROW(C2:K))), "WHERE Col1 <> 0"),
      MMULT(
        ...
      ) /
      MMULT(
        ...
      )
    },
    2,
    0
  ))
)

Where

• SEQUENCE(MAX((C2:K <> "") * ROW(C2:K)) - 1, 1, ROW(C2)) is an array of row numbers from the 2nd one to the last none-empty one. We won't be filling all the rows down with empty strings.
• QUERY(UNIQUE(FLATTEN((C2:K <> "") * ROW(C2:K))), "WHERE Col1 <> 0") is an array of non-empty row numbers with that 0 filtered out used as keys for search.
• IFNA will return an empty string to put alongside an empty data row.

FINAL FORMULA

Putting it all together:

=ARRAYFORMULA(
  IFNA(VLOOKUP(
    SEQUENCE(MAX((C2:K <> "") * ROW(C2:K)) - 1, 1, ROW(C2)),
    {
      QUERY(UNIQUE(FLATTEN((C2:K <> "") * ROW(C2:K))), "WHERE Col1 <> 0"),
      MMULT(
        FILTER(
          FILTER(
            C2:K*1,
            MATCH(
              ROW(C2:K),
              UNIQUE(FLATTEN((C2:K <> "") * ROW(C2:K))),
              0
            )
          ),
          MATCH(
            SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)),
            UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)))),
            0
          )
        ),
        SEQUENCE(
          ROWS(
            QUERY(
              UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)))),
              "WHERE Col1 <> 0"
            )
          ),
          1,
          1,
          0
        )
      ) /
      MMULT(
        FILTER(
          FILTER(
            (C2:K <> "")*1,
            MATCH(
              ROW(C2:K),
              UNIQUE(FLATTEN((C2:K <> "") * ROW(C2:K))),
              0
            )
          ),
          MATCH(
            SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)),
            UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)))),
            0
          )
        ),
        SEQUENCE(
          ROWS(
            QUERY(
              UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)))),
              "WHERE Col1 <> 0"
            )
          ),
          1,
          1,
          0
        )
      )
    },
    2,
    0
  ))
)

A few details

• INDEX could be used instead of ARRAYFORMULA for brevity (thanks @player0, taught me that a few months ago), but I like unambiguity of ARRAYFORMULA.
• I use SEQUENCE to construct a column or a row of 1s to be explicit, for clarity. For example, this one

SEQUENCE(
  ROWS(
    QUERY(
      UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)))),
      "WHERE Col1 <> 0"
    )
  ),
  1,
  1,
  0
)

could be replaced with

SIGN(
  QUERY(
    UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)))),
    "WHERE Col1 <> 0"
  )
)

which is a bit shorter. There is also a way demonstrated here by @player0 of raising to the power of 0:

QUERY(
  UNIQUE(FLATTEN((C2:K <> "") * SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)))),
  "WHERE Col1 <> 0"
)^0

but (it is just my speculation) I think SEQUENCE's internal implementation should be simpler then the operation of raising to a power.

• I use range C2:K which is one column more than there actually exist on the sheet. Not only it gives a range of all the columns to the right of C2 and all the rows down from it, but it also updates in case of adding another column to the right of the sheet: a demo. Though it does not get to be highlighted. This C2:K can almost perfectly (there will be a problem in case there is actually ZZZ column present on a sheet) replace those approaches:

INDIRECT("C2:" & ROWS(C:C))

OFFSET(C2,,, ROWS(C2:C), COLUMNS(C2:2))

• There is a small drawback in using C2:K: =ARRAYFORMULA(COLUMN(C2:K)) will return an array of column numbers even for non-existing ones, so we need to use =SEQUENCE(1, COLUMNS(C2:K), COLUMN(C2)) instead.

I think there is a simple answer for row-wise average using VLOOKUP and QUERY.

This one is in B2:

=ARRAYFORMULA(
  IFNA(
    VLOOKUP(
      ROW(B2:B),
      QUERY(
        {
          FLATTEN(ROW(C2:J) + SEQUENCE(1, COLUMNS(C2:J),,)),
          FLATTEN(C2:J)
        },
        "SELECT Col1, AVG(Col2)
         WHERE Col2 IS NOT NULL
         GROUP BY Col1"
      ),
      2,
      0
    )
  )
)

• This could be easily changed for max, min, sum, count - just change aggregation function inside QUERY statement.
• Same approach could be used for column-wise aggregation.
• FLATTEN(C2:J) could be changed to:
  • FLATTEN(--C2:J) to treat empty cells as 0s;
  • FLATTEN(IFERROR(1/(1/C2:J))) to exclude 0s from average.
• If there are no intermediate empty rows, VLOOKUP could be removed from the formula, as well as Col1 from SELECT statement.
• There's a shorter version (thanks @MattKing!) without VLOOKUP and WHERE Col...:

=ARRAYFORMULA(
  QUERY(
    {
      FLATTEN(ROW(C2:J) + SEQUENCE(1, COLUMNS(C2:J),,)),
      FLATTEN(IFERROR(1/(1/C2:J)))
    },
    "SELECT AVG(Col2)
     GROUP BY Col1
     LABEL AVG(Col2) ''"
  )
)

I use C2:J range having columns up to I:I, some details on that:

• Range C2:J which is one column more than there actually exist on the sheet. Not only it gives a range of all the columns to the right of C2 and all the rows down from it, but it also updates in case of adding another column to the right of the sheet: a demo. Though it does not get to be highlighted. This C2:J can almost perfectly (there will be a problem in case there is actually ZZZ column present on a sheet) replace those approaches:

INDIRECT("C2:" & ROWS(C:C))

OFFSET(C2,,, ROWS(C2:C), COLUMNS(C2:2))

• There is a small drawback in using C2:J: =ARRAYFORMULA(0 * COLUMN(C2:J)) will return an array of column numbers even for non-existing ones (multiplied by 0), so we need to use =SEQUENCE(1, COLUMNS(C2:J),,) instead.

@player0, any thoughts on this?