# Can I use standard deviation of past data set to project variations in the future knowing that the mean value will be different?

I have monthly sales data for past 3-years, so 36 data points. Let's just say that the mean value is 50 units per month, and the standard deviation is 8.5

Now, for the next year the management has set the monthly sales target to be 75 units. Can I just pick the standard deviation from the historical data and use it for next year projection without any modification?

Note that previously the mean value was 50 and stdev was 8.5, but now the mean value is forced to be 75. Can I still use 8.5 as the stdev?

The stdev is required to calculate the amount of safety stock we should have in our inventory planning.

• I would use $8.5\cdot\frac{75}{50}=12.75$ but I base it on nothing – Djura Marinkov Sep 22 '17 at 5:56
• @DjuraMarinkov does that means there is direct proportionality between the stdev and the mean value? – JohnDoe Sep 22 '17 at 6:17
• Most probable it is direct proportionality, but who knows? No way that std variation will remain same. What if you increase sales to 100000? More customers more variation – Djura Marinkov Sep 22 '17 at 6:26
• I would think that it depends on why or how stocks sales go up to 75 units. For example, if $X$ is the distribution of monthly sales, and $Y$ is the distribution of the new target sales, then it is possible that $Y=X+25$ or it's possible that $Y=1.5X$, both yielding different variance (and indeed standard deviation). It's best to model appropriately using all the information you have. – Jihoon Kang Sep 22 '17 at 6:39
• @JihoonKang Basically it's just management's target, most likely just by doing some more intense marketing. I guess the situation is closer to the Y = X + 25 in this case. – JohnDoe Sep 22 '17 at 7:08