MAD Forecast Error Calculation Formula

[kotaroumehara]

Dear experts,

When calculating forecast error, I use the formula from SAP knowledge article.

• MAD = AVG( |Forecast - Sales| )
• CV = 1.25 x ( MAD / MAX [ AVG(Forecast) or AVG(Sales) ] )

Reference: 2556745 - MAD Forecast Error Calculation Defined - IBP for Inventory - SAP ONE Support Launchpad

The question is that I want to know why "1.25" is used in this formula.

Through my investigation, I haven't had figured out what the number meant.

Please let me know if you have any ideas.

Best Regards,

Kotaro

[lev_degtyarov]

Hello,

Typically: CV = σ / average value, where σ is a standard deviation.

Then you put σ = 1.25 MAD in the formula above and receive CV = 1.25 MAD / average value

Below is a simple explanation why in case of normal distribution you can use equation σ = 1.25 MAD.

[piyush_parekh]

Hi Kotaro,

For normally distributed data, mean deviation is sqrt (2/pi) times std. deviation which comes around 0.79. 1/0.79 = 1.25

Refer below link for reference.

https://mathworld.wolfram.com/MeanDeviation.html

Regards,

Piyush