Q: If a population increases from 1,000 to 1,300, what is the relative change in population?

$$\frac{1300 - 1000}{1000} \times 100\% = 30\%$$

Q: A store offers a 20% discount on a jacket originally priced at $50. What is the sale price?

$$50 - (0.20 \times 50) = 50 - 10 = 40$$

Q: The life expectancy in Country A is 82 years and in Country B is 75 years. Using Country A as the reference, what is the relative difference?

$$\frac{75 - 82}{82} \times 100\% = -8.54\%$$

Q: A population triples from 200 to 600. What percentage 'of' the original population is the new population?

$$\frac{600}{200} \times 100\% = 300\%$$

Q: If 40% of voters in Carson City are Republicans and Freetown has 25% more Republicans (relative change), what percentage of Freetown voters are Republicans?

$$40\% + (0.25 \times 40\%) = 40\% + 10\% = 50\%$$

Q: A news report says, 'Market share for electric cars was up 110% to 8.6%.' If last year's market share was 8.6%, what was the prior year's market share?

$$\text{Let } x \text{ be prior year.} \\ 8.6\% = x + 1.10x = 2.10x \\ x = \frac{8.6\%}{2.10} = 4.10\%$$

Q: A statistician reports a change from 15% to 18%. What is the relative change?

$$\frac{18\% - 15\%}{15\%} \times 100\% = 20\%$$

Q: A city’s population grew from 50,000 to 75,000. What is the relative change?

$$\frac{75,000 - 50,000}{50,000} \times 100\% = 50\%$$

Question 1

A survey reports that 60% of 800 respondents prefer online shopping. How many respondents prefer online shopping?

Accepted Answer

$$800 	imes 0.60 = 480$$

Question 2

If a population increases from 1,000 to 1,300, what is the relative change in population?

Accepted Answer

$$\frac{1300 - 1000}{1000} 	imes 100\% = 30\%$$

Question 3

A store offers a 20% discount on a jacket originally priced at $50. What is the sale price?

Accepted Answer

$$50 - (0.20 	imes 50) = 50 - 10 = 40$$

Question 4

Convert the fraction $$\frac{3}{8} to a $$percentage.

Accepted Answer

$$\frac{3}{8} = 0.375 \rightarrow 37.5\%$$

Question 5

The life expectancy in Country A is 82 years and in Country B is 75 years. Using Country A as the reference, what is the relative difference?

Accepted Answer

$$\frac{75 - 82}{82} 	imes 100\% = -8.54\%$$

Question 6

A population triples from 200 to 600. Which statement is correct?

Accepted Answer

The new population is 200% more than the original population.

Question 7

A population triples from 200 to 600. What percentage 'of' the original population is the new population?

Accepted Answer

$$\frac{600}{200} 	imes 100\% = 300\%$$

Question 8

If 40% of voters in Carson City are Republicans and Freetown has 25% more Republicans (relative change), what percentage of Freetown voters are Republicans?

Accepted Answer

$$40\% + (0.25 	imes 40\%) = 40\% + 10\% = 50\%$$

Question 9

If 40% of voters in Carson City are Republicans and Freetown has 25 percentage points more Republicans (absolute change), what percentage of Freetown voters are Republicans?

Accepted Answer

$$40\% + 25\% = 65\%$$

Question 10

A news report says, 'Market share for electric cars was up 110% to 8.6%.' If last year's market share was 8.6%, what was the prior year's market share?

Accepted Answer

$$	ext{Let } x 	ext{ be prior year.} \ 8.6\% = x + 1.10x = 2.10x \ x = \frac{8.6\%}{2.10} = 4.10\%$$

Question 11

Convert 0.27 to a percentage.

Accepted Answer

$$0.27 	imes 100 = 27\%$$

Question 12

A statistician reports a change from 15% to 18%. What is the absolute change?

Accepted Answer

$$18\% - 15\% = 3\%$$

Question 13

A statistician reports a change from 15% to 18%. What is the relative change?

Accepted Answer

$$\frac{18\% - 15\%}{15\%} 	imes 100\% = 20\%$$

Question 14

A city’s population grew from 50,000 to 75,000. What is the absolute change?

Accepted Answer

$$75,000 - 50,000 = 25,000$$

Question 15

A city’s population grew from 50,000 to 75,000. What is the relative change?

Accepted Answer

$$\frac{75,000 - 50,000}{50,000} 	imes 100\% = 50\%$$

Question 16

A store increases the price of a product from $$40 to 50. $$What is the relative change?

Accepted Answer

$$\frac{50 - 40}{40} 	imes 100\% = 25\%$$

Question 17

If a statistician says a rate increased by 5 percentage points, what kind of change is this?

Accepted Answer

An absolute change

Question 18

If a statistician says a rate increased by 5 percent, what kind of change is this?

Accepted Answer

A relative change

Question 19

A survey of 514 people finds that 90% believe grooming is important. How many people is this?

Accepted Answer

$$514 	imes 0.90 = 462.6 \approx 463$$

Uses of Percentages in Statistics: Measurement and Interpretation

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