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Why is it said that if you add percents you often obtain incorrect results?
Wiki User
∙ 10y ago
It may refer to the sum of percentages using 'whole number' approach.
For instance:
In a class A of 20 students only two students are redheaded, i.e. 10% of the students are redheaded. In a class B of 30 students only three students are redheaded, i.e. 10% of the students are redheaded. All students of the class A and all students of the class B are in assembly hall. What is the percentage of redheaded student in the assembly hall?
To answer the question the sum of both class percentages (10%+10%=20%) cannot be used.
You cannot even express the class percentages in fractions and sum them (10/100 + 10/100=20/100=20%).
The easiest way to calculate the percentage of the redheaded students in the assembly hall is to calculate the percentage from scratch ((2+3)/(20+30)=0.10=10%) and not to use the class percentages.
Another example of problem with the summation of percents are consequent percentage changes.
The book you want to buy was marked off 30%. Afterwards the book was discounted by 30% again. If you buy the book after the second discount, you save 51% of the original price (not 60%, the sum of the two discounts).
The first discount reduced the price to 70% of the original price. The second discount reduces the discounted price by 30%, i.e. the final price is 49% of the original price (0.7*0.7=0.49=49%). You save 51% (100%-49%).
Percentage decrease followed by percentage increase can cause even more surprising results.
The price of a share decreased by 60% one year. The next year the share price raised by 80%. The net effect was 28% decrease from the original price!
The share price was 40% of the original price after the first year. The next year the price raised by 80% of the lowered price, i.e it was 72% of the original price (1.8*0.4=0.72=72%). The net decrease was 28% (72%-100%).
Wiki User
∙ 10y ago
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