# What should I call these growth rates?

I have a table of sales growth rates by month calculated thus:

$$\text{growth rate}_i=\dfrac{\text{sales in month } i-\text{sales in January}}{\text{sales in January}}$$

What should I call this table? The best I've come up with it "sales growth rates from January by month". Is this ambiguous? Is there a technical term for this?

(I've had almost nothing to do in my life with anything that counts money or statistics for that matter).

• Percentage change in sales between January and month $i$. Apr 8 '14 at 18:36

Some suggestions, besides Alecos':

• Relative sales growth;
• Sales growth ratio between month j and January;

I believe you have a ratio rather than a rate. A ratio has the same measurement unit in numerator and denominator, and a rate does not.

Here are some videos with more insights on this subject.

Consider the following example:

At the column D we have a ratio, similar from what you are doing:

$$\text{Sales growth on month} \hspace{1mm} j = [(\frac{Sales_j}{Sales_{January}}) -1] \times 100$$

So, sales in February increased 25% in relation to January. Sales on March decreased -3% in comparison with the sales from January, and so on.

At column E we have a rate: sales growth by month (which means we have different units on the numerator and the denominator).

We get the values on column E according to the following equation:

$$\text{Sales}\hspace{1mm} \text{on} \hspace{1mm} \text{month} \hspace{1mm} j = \text{Sales}\hspace{1mm} \text{on} \hspace{1mm} \text{January} \times (1 + i)^t$$

where:

t = time in months.
i = sales growth by month.

So in this second example one would have an increase on sales of 25% by month on February, a decrease of -1.3% by month on March, and so on.

First of all, this is not a growth rate. The reason is that the rate is always attached to a time period, e.g. annual or monthly rate. If you fixed $i$, then you could still call your metric a rate assuming that implicitly it's for $i$ months. Since, your $i$ appears to be variable, this is not the growth rate but it's a growth.

You could call your metric percentage change as others suggested, but if you wanted to be more specific you could add a qualifier simple, as opposed to continuously compounded which would have been $\ln(\frac{s_i}{s_J})$

UPDATE: if your $i$ is from a standard interval set such as a month, quarter, year, then you can add month-to-month or quarter-over-quarter qualifier.