# Calculating an annual inflation rate from monthly data

Let's say I have the following inflation data (for 11 months):

"2015-01" = 3.85 "2015-02" = 2.22 "2015-03" = 1.21 "2015-04" = 0.46 "2015-05" = 0.35 "2015-06" = 0.19 "2015-07" = 0.80 "2015-08" = 0.35 "2015-09" = 0.57 "2015-10" = 0.74 "2015-11" = 0.75

Then, how to calculate an annual inflation rate? Somehow I thought that it should something like that:

• divide data by 100 to get decimal values
• sum everything and divide by 11 to get an average monthly value
• raise to 11th degree
• subtract 1.

That somehow results in something like 12.10%, which looks like the right answer but not exactly (the page with data says it's 12.05%).

So, am I right, and if no, then where's my mistake?

• Doing the sum and division gives an arithmetic mean. You want the "compounded growth rate" that would be multiplying the values together and then taking the 11th root to get the geometric mean, I'd suspect. – JB King Dec 11 '15 at 20:07

You don't want to average them, since the rates are compounded and thus multiplicative. In other words, if inflation was 10% one month and 10% the next month, then over the two months prices went up 1.1*1.1 = 1.21 = 21%.

What you should do is divide all the numbers by 100 and add one to all of them to get conversion factors (i.e., so that 0% inflation is converted to the number 1). Then multiply all of the numbers to get an overall conversion factor. To convert that back to a percentage, subtract 1 and then multiply it by 100. So for the first row of your table it would be `1.0385 * 1.0222 * 1.0121 * ...`. When I do this, the results agree with what is shown on the table.

The year-to-date is

``````(1.0385*1.0222*1.0121*1.0046*
1.0035*1.0019*1.008*1.0035*
1.0057*1.0074*1.0075) - 1 = 0.120454 = 12.05 %
``````

For a projection of the annual rate take the geometric mean to find the average monthly rate, then compound it for the annual rate:-

``````gm = (1.0385*1.0222*1.0121*1.0046*
1.0035*1.0019*1.008*1.0035*
1.0057*1.0074*1.0075)^(1/11) = 1.01039

annual rate = gm^12 - 1 = 13.2 %
``````