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Weighted avarage problems with negative numbers and outliers

Problem Solving — algebra and arithmetic
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Newbie | Next Rank: 10 Posts
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by ever! » Sun Feb 11, 2018 12:56 pm
I am trying to calculate a weighted average and I have this information
Revenues for Jan, Feb, Mar: 50, 75, 52
Growth rate (comparing to the previous year) for Jan, Feb, Mar: 2%, 3% and -5%

If I want to calculate weighted average I will do the following ( (50*0,02)+(75*0,03)+(52*(-0,05))/50+75+52

This way I calculated manually growth rate for the first quarter of the year. Revenues for the first quarter are 177. However, I am deeply concerned for the result because of two reasons:

1. number 75 seems like an outlier which can cause the biased result
2. I am not sure what impact a negative percentage of -5% has on the overall result
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Source: — Quantitative Reasoning |
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by DrMaths » Wed Feb 28, 2018 10:26 am
Jan: 50 /1.02 = 49.02 Jan last year
I will assume that it is the weighted average growth rate you are looking for.
Also, based on your question, I assume the growth rates are from last year's (ungiven data) to this year's (given data) revenues.

Feb: 75/1.03 = 72.82 Feb last year
Mar: 52/0.95 = 54.74 Mar last year

So this year, total = 50 + 75 + 52 = 177
and last year, total = 49.02 + 72.82 + 54.74 = 176.58

So the weighted average increase is 177/176.58 = 1.00234
Hence the weighted average growth rate is 0.234%

Is this what you were looking for?

I don't think that 72% is an outlier with a sample size of only 3.
And negative percentages show a decrease from 100%, so -5% means it is now 95% = 0.95
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by ceilidh.erickson » Mon Jul 23, 2018 8:16 am
ever! wrote:I am trying to calculate a weighted average and I have this information
Revenues for Jan, Feb, Mar: 50, 75, 52
Growth rate (comparing to the previous year) for Jan, Feb, Mar: 2%, 3% and -5%

If I want to calculate weighted average I will do the following ( (50*0,02)+(75*0,03)+(52*(-0,05))/50+75+52
You're making a few common mistakes here:

1. You were calculating a percent OF January's revenue, rather than a percent INCREASE. If you want to say that X is 2% more than Y, it is 102% of Y: multiply Y by 1.02, not 0.02. If something is a 2% decrease, then we're left with 98% of the original (100-2). Multiply by 0.98.

2. You're going backwards. We are told this year's revenues, which represent certain percent changes over last year's unstated revenues (as DrMaths pointed out). An unknown amount grew by 2% to get this January's revenue of 50. We do not multiply 50 by 1.02. We say that X(1.02) = 50. To solve for X, divide 50 by 1.02, as DrMaths demonstrated.

Be careful not to make these mistakes on percent change questions in the future!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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