How to calculate weighted averages in Google Sheets?

Question

I have a Google Sheets where products are listed as rows and attributes as columns. Each product's attribute is rated on a scale of 1-10. My last column is an average of these values (i.e. =Average(B2:D2)). This works fine if each attribute has the same weight.

+--------+-------+-------+-------+---------+
|        | Attr1 | Attr2 | Attr3 | Overall |
+--------+-------+-------+-------+---------+
| Prod 1 | 10    | 8     | 9     | 9       |
| Prod 2 | 2     | 10    | 7     | 6.33    |
| Prod 3 | 4     | 6     | 6     | 5.33    |
+--------+-------+-------+-------+---------+

The problem is that I want each attribute to have a different weight. For example, Attr1 might not be important and should only be worth 50%, while Attr3 is very important and should be worth 300%.

+--------+-------------+-------+--------------+---------+
|        | Attr1 (50%) | Attr2 | Attr3 (300%) | Overall |
+--------+-------------+-------+--------------+---------+
| Prod 1 | 10          | 8     | 9            | 8.89    |
| Prod 2 | 2           | 10    | 7            | 7.11    |
| Prod 3 | 4           | 6     | 6            | 5.78    |
+--------+-------------+-------+--------------+---------+

The value for the first row would be:

(10*0.5 + 8*1 + 9*3) / (0.5+1+3) = 8.89

which could be calculated by using:

(
  B2*(IFERROR(REGEXEXTRACT(B1, "\d+"), 100)/100) 
  + C2*(IFERROR(REGEXEXTRACT(C1, "\d+"), 100)/100)
  + D2*(IFERROR(REGEXEXTRACT(D1, "\d+"), 100)/100) 
) / (
  IFERROR(REGEXEXTRACT(B1, "\d+"), 100)/100
  + IFERROR(REGEXEXTRACT(C1, "\d+"), 100)/100
  + IFERROR(REGEXEXTRACT(D1, "\d+"), 100)/100
)

which, as you can see, can become very difficult to manage as more attributes are added. Ideally, I'm looking for a solution that doesn't require creating temporary cells to help with the calculations.

Is there any built in function or a common convention that can help me calculate these weighted averages?

Answer 1

There is no built in function to calculate the weighted average so you have to write a custom function if you want to avoid using too many temporary cells. So here is how you can achieve your goal.

Go to Tools > Scripts > Script editor..., Copy/Paste the bellow code and save it:

function weightedAverage(v, w) {
  var sum_v = 0;
  var sum_w = 0;

  if (v[0].length != w[0].length) {
    return "#ERROR: Incorrect number of values and weights";  
  }

  for (var c = 0; c < v[0].length; ++c) {
    sum_v += v[0][c] * w[0][c]; 
    sum_w += w[0][c]; 
  }

  return sum_v/sum_w;
}​

Use it like:

=weightedAverage(B3:D3,$B$2:$D$2) 

Where B3:D3 are your values and $B$2:$D$2 your weights. It's not error proof (the only check is to make sure both arrays have the same length) but it will do the trick.

In the above example I'm not trying to extract the weights from the title of the attribute, but I'm reading them from the second row (B2:D2) to make our life easier and clearer. The $ is not changing the result of the formula. It's only affecting what's happening when you're copying the formula in another cell. The part of the cell reference following the $ will not change (link for more details). Write the formula once in the cell E3 and Copy it to the rest of the rows to see it in action.

Answer 2

If your weights are in row 2 from B to L, and the data you want to average is in rows 3 and higher, say, then you can use sumproduct as follows:

=sumproduct(B$2:L$2, C3:L3)/sum(B$2:L$2)

Answer 3

Google seemed to have listened. At least in my instance of Google Sheets, the function AVERAGE.WEIGHTED exists. Per the help:

=AVERAGE.WEIGHTED(values,
                  weights,
                  [additional_values, ...],
                  [additional_weights, ...])

Answer 4

Lipis' code was not working for me, so here's an update. This code:

• works with current version of Google Spreadsheets correctly addressing array elements

• checks whether the values are numbers

• has a switch to consider zero values or not

Code:

/**
  v - Values range
  w - Weights range
  z - count zero values?
*/

function weightedAverage(v, w, z) {
  var sum_v = 0;
  var sum_w = 0;

  if (v.length != w.length) {
    return "#ERROR: Incorrect number of values and weights";  
  }

  for (var c = 0; c < v.length; ++c) {
    if (!z && Number(v[c][0])!=0) {
      sum_v += Number(v[c][0]) * Number(w[c][0]); 
      sum_w += Number(w[c][0]); 
    }
  }

  return sum_v/sum_w;
}

Answer 5

Correcting Lipis' code to work for the current version of Google Spreadsheets:

function weightedAverage(v, w) {
  var sum_v = 0;
  var sum_w = 0;

  if (v.length != w.length) {
    return "#ERROR: Incorrect number of values and weights";  
  }

  for (var c = 0; c < v.length; ++c) {
    sum_v += v[c] * w[c]; 
    sum_w += w[c] * 1; 
  }

  return sum_v/sum_w;
}​

Answer 6

ARRAYFORMULA() can calculate a weighted average in Google Spreadsheets (and more).

Storing the weights separately in B2:D2 simplifies reading the formula. Calculating the weighted average for E3 then looks similar to SUMPRODUCT() above (copy/paste for E4 & E5):

=ARRAYFORMULA(sum(B3:D3 * $B$2:$D$2)/sum($B$2:$D$2))

+--------+-------------+-------+-------------+---------+
|        | AttrA (50%) | AttrB | AttrC (300%)| Overall |
| Weight:|        50%  |  100% |        300% |         |
+--------+-------------+-------+-------------+---------+
| Prod 1 |       10    |  8    |       9     | 8.8889  |
| Prod 2 |        2    | 10    |       7     | 7.1111  |
| Prod 3 |        4    |  6    |       6     | 5.7778  |
+--------+-------------+-------+-------------+---------+

Using RegExExtract() to get the weights from $B$1:$D$1 is a simple change in the ARRAYFORMULA(). Replace the simple range with the more complex expression "iferror(regexextract($B$1:$D$1,"\d+"),100)/100" and the formula for E3 becomes (copy/paste for E4 & E5):

=ARRAYFORMULA(sum(B3:D3 * iferror(regexextract($B$1:$D$1,"\d+"),100)/100)/sum(iferror(regexextract($B$1:$D$1,"\d+"),100)/100))

N.B. That regexp requires attribute names without numbers; so, use AttrA, AttrB & AttrC instead of Attr1, Attr2 & Attr3.

Answer 7

Having read your question carefully,

Ideally, I'm looking for a solution that doesn't require creating temporary cells to help with the calculations.

I came up with this solution, that uses no temporary cells.

Formula

weights = ARRAYFORMULA(IFERROR(VALUE(REGEXEXTRACT($B$1:$D$1,"\((\d+)")),100))

=SUMPRODUCT(B3:D3, weights) / SUM(weights)

copy / paste
=SUMPRODUCT(B2:D2, ARRAYFORMULA(IFERROR(VALUE(REGEXEXTRACT($B$1:$D$1,"\((\d+)")),100)))/SUM(ARRAYFORMULA(IFERROR(VALUE(REGEXEXTRACT($B$1:$D$1,"\((\d+)")),100)))

Screenshot

Explained

The REGEXEXTRACT will extract the value in the header after the first straight bracket and VALUE will convert it into a number. The IFERROR will set the value at 100 if nothing is found and the ARRAYFORMULA will make it possible to select a range, rather than individual cells.

Example

I've created an example file for you: How to calculate weighted averages in Google Spreadsheets?

Answer 8

Since the accepted answer is using Google Apps Script, I also created a little snippet.

Code

function weightedAverage(v, w) {
  var weights = [], sumWeights = 0;
  for(var k = 0, kLen = w[0].length; k < kLen; k++) {
    var m = w[0][k].match(/\((\d+)/), value;
    if(!m) {
      value = 100;
    } else {
      value = Number(m[1]);
    }
    weights.push(value);
    sumWeights += value;
  }

  var output = [];
  for(var i = 0, iLen = v.length; i < iLen; i++) {
    var sumProduct = 0;
    for(var j = 0, jLen = v[0].length; j < jLen; j++) {
      sumProduct += v[i][j] * weights[j]; 
    }
    output.push(sumProduct / sumWeights);
  } 
  return output;
}

Screenshot

Note

The script will follow the same logic as presented in this post. The main advantage is that it will calculate the overall values at once.

Example

I've created an example file for you: How to calculate weighted averages in Google Spreadsheets?

Answer 9

For simple weighted averages, you can just add the cell value multiple times. Like if you want A1 to be 75% and B1 to be 25%, you can put in =AVERAGE (A1,A1,A1,B1). So specifically for yours, it would be =AVERAGE (B2,C2,C2,D1,D2,D2,D2,D2,D2,D2), which would weigh B2 as half of C2 (50%) and D2 as 3x C2 (300%).

More complicated stuff is above my pay grade. :)

Answer 10

Actually both versions Average.weighted and sumproduct give the same result:

AVERAGE.WEIGHTED("Values","Weight")

SUMPRODUCT("Numbers","Weight")/sum("Weight")

So I rather use the first one since is way more simple to handle it, however I don't know how to add other weights to this formula.

This is the tooltip, but don't know how to add only weights and not additional values

AVERAGE.WEIGHTED(values, weights, [additional_values, ...], [additional_weights, ...])

Answer 11

There is quite simple way using only given functions.

=(sumproduct(E5:E9;G5:G9)/sum(E5:E9))   

where E contents is number of points and G the importance of those points.