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LSP 120. Percentages. Percentages. There are six basic types of percentage problems: Creating a percentage Percentage of Percentage change Percent more than Successive percentage change Reverse percentage change And one simple ratio: Times more than. 1. Creating a Percentage.

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### LSP 120

Percentages

Percentages
• There are six basic types of percentage problems:
• Creating a percentage
• Percentage of
• Percentage change
• Percent more than
• Successive percentage change
• Reverse percentage change
• And one simple ratio:
• Times more than
1. Creating a Percentage
• In Chicago in 2000 there were approx 1.053 million African Americans, 907,000 whites, 754,000 Hispanics, and 181,000 others. What percentage of Chicagoans were of Hispanic origin?
• Remember: part over whole
• 754,000 / (1,053,000+907,000+754,000+181,000) = 0.26 or 26%
• Another example: AgeDistribution.xls
2. Percentage Of
• 54% of DePaul’s student body is female. DePaul has approx 21,000 students. Approximate how many females attend DePaul.
• Multiply total by percentage
• 21,000 * 0.54 = 11340
2. Percentage Of
• 65% of US citizens have xyz insurance
• Of those that have xyz insurance, 20% of those have the premium policy
• What percentage of US citizens have the premium policy?
3. Percentage Change
• You are examining one thing and how it has changed over time
• Chicago’s population grew from 2.78 million in 1990 to 2.90 million in 2000. By how many percent did it grow?
• Divide difference by original value

(2.90 – 2.78) / 2.78 = 0.043 = 4.3%

3. Percentage Change
• In 1996, 94,007 tons of waste were recycled in Chicago’s blue bag program. In 2000, 296,363 tons were recycled. By how many percent did it increase?
• Divide difference by original value
• (296,363 – 94,007) / 94,007 = 2.15 = 215%
4. Percentage More Than
• You are comparing two different examples of something
• The life expectancy in Canada is 79.1 years while it is 76.0 years in the U.S. By how many percent is the life expectancy in Canada higher than in the U.S.?
• Divide difference by latter value stated in problem

(79.1-76.0) / 76.0 = 0.041 = 4.1%

4. Percentage More Than
• The dropout rate of school X is 23.5% while the dropout rate of school Y is 18.2%. By how many percent is the dropout rate of school X higher than the dropout rate of school Y?
• Divide difference by latter value

(23.5 – 18.2) / 18.2 = 0.29 = 29%

4. Percentage More Than
• Country X has 3.2 cars per family
• Country Y has 1.4 cars per family
• By how many percent is the average cars per family for country X greater than country Y?
5. Successive Percentage Change
• You are buying a sweater at the store. The tag says it is 25% off. The sign above the rack says take another 20% off the tag price. What is total % off of the sweater?
• 100% - 25% = 75%
• Take another 20% off of 75% (0.2 * 0.75 = 0.15), so that’s another 15% off.
• Total: -25% + -15% = -40%
• Example: What if sweater originally \$100?
5. Successive Percentage Change
• Spot prices for crude oil are rather volatile. From 1998 to 1999, spot prices decreased by 28%. From 1999 to 2000, they increased by 16%. What was the percentage change over the two year period from 1998 to 2000?
• 100%-28% = 72% (first year)
• 72%*16% = 11.52% (second year)
• -28% + 11.52% = -16.48 % total increase
5. Successive Percentage Change
• Spot prices for crude oil are rather volatile. From 1998 to 1999, spot prices decreased by 28%. From 1999 to 2000, they increased by 106%. What was the percentage change over the two year period from 1998 to 2000?
• 100%-28% = 72% (first year)
• 72%*106% = 76.3% (second year)
• -28% + 76.3% = 48.3% total increase
5. Successive Percentage Change
• Another way to think of successive percentage change

Given% Actual % Inc Current %

- - 100%

20% 20% 120%

30% 36% 156%

10% 15.6% 171.6%

-20% -34.3% 137.3%

Now to find the total percentage change, add 20%+36%+15.6%

-34.3%, giving you 37.3%. Or, subtract the original 100%

from the final % of 137.3%, leaving a 37.3% increase.

If it helps, change Actual % Inc and Current % to Actual \$ Inc

and Current \$ and treat these values are dollar values.

5. Successive Percentage Change
• The stocks you are holding dropped in value by 30% the first year.
• In the second year, they increased by 12%.
• In the third year they increased by 8%.
• What was the total percentage change over the three year period? (-15.33%)
6. Reverse Percentage Change
• According to the official 2000 census, the Hispanic population of the U.S. was 35,305,818. It rose by 57.9% from 1990 to 2000. What was the Hispanic population in 1990? old * (1 + %change) = new

x * (1+0.579) = 35,305,818

x * (1.579) = 35,305,818

x = 35,305,818 / 1.579

x = 22,359,606

Percentage change (+)

Current (or new) Value (2000)

Original (old) Value (1990)

6. Reverse Percentage Change
• You just spent \$46.23 for a new pair of jeans. This was the total price with sales tax. You know that sales tax was 7.5%. What was the price of the jeans before the tax was added?

x * ( 1 + 0.075) = 46.23

x * 1.075 = 46.23

x = 46.23 / 1.075 = 43.00

6. Reverse Percentage Change
• The cost of tuition dropped by 14% over the last year at University Lah-Dee-Dah.
• This year tuition costs \$23,000.
• What was the cost of tuition last year?

X * (1 – 0.14) = 23,000

Times More Than
• Not a percentage, but a simple ratio
• How many times more is the life expectancy of Canada higher than the life expectancy in the U.S.?
• Divide former by latter
• 79.1 / 76.0 = 1.041
Times More Than
• How many times is the dropout rate of school X higher than the dropout rate of school Y?
• Divide former by latter
• 23.5 / 18.2 = 1.29
Finally
• If you enter a formula, you can copy it down or over
• Let’s see how to use the Thematic Mapping Tool
• Use the data set RegisteredVoters2000.xls