# How do I calculate a cumulative reducing percentage for forecasting?

• MHB
• gazzap
In summary, the conversation discusses a maths problem where a target percentage must be achieved by the end of the year. The current cumulative result is above the target and the speaker is looking for a formula to calculate the result needed in the remaining months to hit the target exactly. The example provided shows that an average of 73.9% must be achieved in the remaining months. The speaker also mentions that the change in cumulative result decreases each month until the target is hit and is unsure of the name of this problem. They are seeking assistance in finding a formula to calculate the needed result.
gazzap
I have a maths problem that has confused me.
Each month I have a performance score. Month by month those scores are added together to make a cumulative score of the year to date.
There is a target (percentage) that must be achieved by the year end. Based on the current cumulative result I need to find what the result has to be in all of the remaining months in order to hit the target exactly.

For example
Month 1 result: 93 out of 100 (93%)
Month 2 result: 71 out of 100 (cumulative result is now 82%, 164 out of 200)

Target for year is 75%.

So, in the remaining 10 months, the result each month would have to be less than 75% (because it is currently 7% above the target). But what is the formula to calculate that figure?
Each month going forward, the real result will be entered, and of course this will have an effect on this figure.
I know the answer to the example is 73.9%, achieved purely using trial and error but I cannot create the formula to find the answer.
Using this figure I can see that the cumulative result changes more in the first month than the second and the second is more than the third and so on. ie the change is in ever decreasing amounts until the target is hit.
I don't know what the name of this maths problem is.
Can anyone help?

gazzap said:
I have a maths problem that has confused me.
Each month I have a performance score. Month by month those scores are added together to make a cumulative score of the year to date.
There is a target (percentage) that must be achieved by the year end. Based on the current cumulative result I need to find what the result has to be in all of the remaining months in order to hit the target exactly.

For example
Month 1 result: 93 out of 100 (93%)
Month 2 result: 71 out of 100 (cumulative result is now 82%, 164 out of 200)

Target for year is 75%.

So, in the remaining 10 months, the result each month would have to be less than 75% (because it is currently 7% above the target). But what is the formula to calculate that figure?
You need to use "raw" numbers rather than percentages but if that "out of 100" stays constant, then you can just treat the percentages as if they were "raw" numbers. If you want 75% 0ver the 12 months of the year, then you want a raw score if 0.75*1200= 900. You already have 93+ 71= 164, as you say. So you want a total of 900- 164= 736 over the next 10 months. That is an average of 73.6 for each month so you will want 73.6%, not 73.9%, of 100 each month.

Each month going forward, the real result will be entered, and of course this will have an effect on this figure.
I know the answer to the example is 73.9%, achieved purely using trial and error but I cannot create the formula to find the answer.
Using this figure I can see that the cumulative result changes more in the first month than the second and the second is more than the third and so on. ie the change is in ever decreasing amounts until the target is hit.
I don't know what the name of this maths problem is.
Can anyone help?

Unfortunately the number isn't always out of 100 each month. I was using that to simplify the example so that the number would equal the percentage in the example but in reality the numbers are basically random. If I knew the total for the year was going to be out of 1200 then yes it would be far easier.

## 1. How do I calculate a cumulative reducing percentage for forecasting?

In order to calculate a cumulative reducing percentage for forecasting, you will need to first determine the initial value and the final value. Then, subtract the final value from the initial value to find the total amount of change. Next, divide the total amount of change by the initial value and multiply by 100 to find the reducing percentage. Finally, subtract this reducing percentage from 100 to get the cumulative reducing percentage.

## 2. What is the purpose of calculating a cumulative reducing percentage for forecasting?

The purpose of calculating a cumulative reducing percentage for forecasting is to track the overall reduction in a certain variable over a period of time. This can be useful in predicting future trends and making informed decisions.

## 3. What factors should be considered when calculating a cumulative reducing percentage for forecasting?

When calculating a cumulative reducing percentage for forecasting, it is important to consider the time period being analyzed, the accuracy of the data, and any external factors that may have influenced the reduction.

## 4. Can a cumulative reducing percentage be negative?

Yes, a cumulative reducing percentage can be negative. This would indicate an increase in the variable being analyzed rather than a decrease.

## 5. How often should a cumulative reducing percentage be recalculated?

The frequency of recalculating a cumulative reducing percentage for forecasting depends on the specific situation and the purpose of the analysis. It is generally recommended to recalculate it at regular intervals to track any changes, but it may also be necessary to recalculate it more frequently if there are significant changes in the data or external factors.

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