(12C) Geometric Mean with Percentage
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07-13-2024, 05:26 AM
Post: #1
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(12C) Geometric Mean with Percentage
To calculate the overall geometric mean percentage increase,
you can use the following formula: GM% = [ n√(1+r1)(1+r2)(1+r3)...... ] - 1 -------------------------------------------------------------------- Procedure: Initialize by [f] REG to clear all Store Register Input Percent Data then [R/S] display show Data Count 1, 2 .... n When done press 0 [R/S] display answer GM% --------------------------------------------------------------------- Example: FIX 2 An investor has annual return of 5%, 10%, 20%, -50%, and 20%. [f] REG 5 [R/S] display 1 10 [R/S] display 2 20 [R/S] display 3 -50 [R/S] display 4 20 [R/S] display 5 0 [R/S] display answer -3.62 This results in a -3.62% annual return. -------------------------------------------------------------------------- Program: Quote:01 ENTER Gamo 7/2024 |
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07-13-2024, 07:08 PM
Post: #2
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RE: (12C) Geometric Mean with Percentage
You could just add 100 to the percentages, calculate the geometric mean and subtract 100 from the result.
Also the logarithm could be used to translate the geometric to the arithmetic mean: \( \log(\sqrt{x \cdot y}) = \frac{\log{x} + \log{y}}{2} \) This program enters the data: Code: 01- 26 : EEX To calculate the geometric mean use: Code: 01- 43 0 : g x̄ |
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07-13-2024, 08:30 PM
Post: #3
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RE: (12C) Geometric Mean with Percentage
(07-13-2024 07:08 PM)Thomas Klemm Wrote: You could just add 100 to the percentages, calculate the geometric mean and subtract 100 from the result. Or, subtract 100% from each calculation: (1+r1) * (1+r2) - 1 = r1*(1+r2) + r2 Code: % 5 Enter 10 R/S → 15.5 20 R/S → 38.6 -50 R/S → -30.70 20 R/S → -16.84 Investment return, "average" = -16.84 / 5 = -3.37% APY = ((1 + -16.84/100)^(1/5)-1) * 100% ≈ -3.62% Note: Arithmetic mean of returns = (5+10+20-50+20)% / 5 = 1%, yet ROI is negative! |
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07-14-2024, 11:45 AM
(This post was last modified: 07-14-2024 11:55 AM by Gamo.)
Post: #4
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RE: (12C) Geometric Mean with Percentage
Program update with added feature to include the arithmetic mean.
--------------------------------------------------------------------------- Procedure: For a new computation, clear statistic registers by pressing [f] ∑ Enter a percentage and press [R/S] Data Count is temporary displayed and then displaying geometric mean of percentage. Press [X<>Y] for Arithmetic Mean Repeat percentage entry using the [R/S] key for each elements of the list. ----------------------------------------------------------------------------- This example is from HP-12C User's Handbook on Page 30 With this example I will calculate the Percent of Total with each answer of that Percentage of Total this program also calculate the Geometric Mean with percentage. Last month, your company posted sales of$3.92 million in the U.S., $2.36 million in Europe, and $1.67 million in the rest of the world. What percentage of the total sales of all three region and What is the Geometric Mean of that percentage? [f] Σ 3.92 [ENTER] 2.36 [+] display 6.28 1.67 [+] display total 7.95 [STO] 0 // Store Total Amount for later use to find %T While 7.95 on display 3.92 [%T] display answer 49.31 [R/S] display 1 pause and display 49.31 [RCL] 0 2.36 [%T] display answer 29.69 [R/S] display 2 pause and display 39.15 [RCL] 0 1.67 [%T] display answer 21.01 [R/S] display 3 pause and display 32.82 Data, %T, GM% 3.92, 49.31%, 49.31% 2.36, 29.69%, 39.15% 1.67, 21.01%, 32.82% // Final Answer for the GM% is 32.82% ---------------------------------------------------------------- Program: Quote:00- Thanks C.Ret for this update edition Gamo |
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07-14-2024, 12:20 PM
Post: #5
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RE: (12C) Geometric Mean with Percentage
Or then you combine my two code snippets with the PSE command:
Code: 01- 26 : EEX |
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07-22-2024, 09:53 AM
(This post was last modified: 07-22-2024 09:55 AM by Gamo.)
Post: #6
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RE: (12C) Geometric Mean with Percentage
Geometric Mean with Percentage using TVM
Each new data set clear all Statistic, Financial and Store Registers To Clear: [f] Σ [f] FIN [f] REG Example: FIX 2 An investor has annual return of 5%, 10%, 20%, -50%, and 20%. Entering the data above: 5 [ENTER] 1 [%] [LSTx] [+] display 1.05 [R/S] display 1 10 [ENTER] 1 [%] [LSTx] [+] display 1.10 [R/S] display 2 Do the rest the same way and the final data count should be 5 If you can do percent and add 1 in your head just enter the amount and press [R/S] When done press 0 [R/S] display answer -3.62% Program: Quote:01 STO 0 Remark: If you remember all the steps needed no need to use as a program demonstrated here. Gamo 7/2024 |
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07-22-2024, 11:20 AM
Post: #7
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RE: (12C) Geometric Mean with Percentage | |||
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