You have a bunch of numbers in a business report (could be sales, could be demand, could be cost, you name it) and at the bottom line there is a number showing the Monthly Average of the data set.You want to summarize the average for the whole year, so you add up all the Monthly Averages, divide the sum by the total number of months. Boom: behold the “Yearly Average”, right?
Maybe.
A common mistake I did in the past and observed people doing it in data analysis is averaging the averages. The reason taking an average of averages is wrong is that most often than not, it doesn’t take into account how many units / sample size went into each average.
For example : Let say we have demand for a product in two different regions, Central and South. The average selling cost per unit of the product in Central is RM50, and the average selling cost per unit in South is RM100. Now let say demand volume in Central is 100 units, and demand volume in South is 1,000 units.
Taking the average of the two averages would give us RM75 as the overall average selling costs.
- (RM50 +RM 100) /2
- RM 150 / 2
= RM 75
However, if we take volume into account, the average would be RM 95!
= (RM50*100 + RM100*1,000) / 1,100
= RM105,000 / 1100
= RM 95
Now what if we had bigger set of volumes and we were trying to budget or plan for next year? Budgeting 1Mil units in sales with RM75 in cost per unit will give you a budget of RM75 Mil, while budgeting with RM95 as cost per unit will give you a budget of RM95 Mil.
A difference of over RM20 Mil!
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It may not always be wrong, though. It really depends on your interpretation, how you want the data to communicate to people reading it.
For example let say:
- School A has 10,000 students with an average CGPA of 3.75.
- School B has 1,000 students with an average CGPA of 2.00.
Now you may either get the average CGPA with regards to the number of school:
(3.75 + 2.00) / 2 = 2.88
or you may get the average CGPA with regards to the number of students :
(3.75*10000) + (2.00*1000) / 11,000 = 3.59
Both numbers make sense but have, of course, completely different implications and interpretations.
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In conclusion, next time you want to do something as easy as averaging the data set, be mindful as you might do it wrong!
