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Question
Hi Janet,

I am two numbers: a forecast number and an actual number. I'd like to measure the percent difference of the actual number in relation to the forecast number. I'd like to be able to say "The forecast number was x% higher/lower than the actual number." And, if different, "The actual number was x% higher/lower than the forecast number."

The numbers will be positive, negative, and in some cases zero.

Sample Data:

Forecast Number          Actual Number
161          157
74          0
24          -12
-4          143

Thanks for your time!

Answer
It's easier to show than to explain.
Forecast = 161
Actual = 157

Expressing forecast as a percentage of actual:
 difference = forecast - actual = 161 - 157 = 4
 difference/actual = 4/157 ≅ 0.0255 = 2.55%
The forecast was 2.55% higher than the actual.

Expressing actual as a percentage of forecast:
 difference = actual - forecast = 157 - 161 = -4
 difference/forecast = -4/161 ≅ -0.0248 = -2.48%
The actual was 2.48% lower than forecast.

The others are calculated the same way.

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Janet Yang

Expertise

I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

Experience

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

Publications
Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language

Education/Credentials
I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.

Past/Present Clients
George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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