# Normalizing data

i have a different sample size n for every month

for example i have 13890 one month then 17756, then 21425

the data every month for example 13890 is broken down into:

48 chairs, 12 tables, 2 couches etc...


next month we have similar metrics like

3 chairs, 23 tables, 4 couches etc..


i would like to know how i am doing with the furniture in relation to the total per month

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Do you mean you want the percentage of the n in that month that belongs to each furniture category? If so, can't you take the N for each month and divide all of the values from that month by N?

For example, your first case would be: 0.0034557235 0.0008639309 0.0001439885 and your second case (where N = 17756) would be 0.0001689570 0.0012953368 0.0002252760.

Or do you want a comparison of your observed values to your expected values? If that is the case you can construct a table with furniture type as columns and months as rows. For each cell you can take the (sum of values in the row to which it belongs) * (sum of values in the column to which it belongs) and divide by the total number of values you have. That will give you the expected value for the cell. If you subtract that from your initial value it will tell you how many more or less of each type of furniture you had than expected given the type of furniture it is and the month in which you made your observation.

For example, consider this source data

Month  Chairs  Tables  Couches  Other   Total
1      48      12      2        13828   13890
2      3       24      4        17725   17756
Total  51      36      6        31553   31646
48 chairs, 12 tables, 2 couches


It would be calculated like so (with the ?? marking values that still need to be calculated)...

Month  Chairs                 Tables  Couches  Other   Total
1      (51*13890)/31646=22.38     ??       ??     ??   13890
2      (51*17756)/31646=28.61     ??       ??     ??   17756
Total  51                         ??       ??     ??   31646


Letting you know that in Month 1 there were 48-22.38=25.62 more chairs than expected and that in Month 2 there were 3-28.61=-25.61 more chairs than expected - but to make more sense we can flip the sign and the terminology and say there were 25.61 fewer chairs than expected.

For more details consider looking here.

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