Numeracy & Quantitative Reasoning Flashcards

A politician states: 'Our city's test scores rank in the top 10 nationally.' The city has 500 school districts nationwide. How many districts rank at or above this city?

Answer: 50

Top 10% of 500 districts = 50 districts, meaning up to 50 districts rank at or above the city.

A research report states 'the correlation between ice cream sales and drowning rates is r = 0.9.' What is the most critical thinking–appropriate interpretation?

Answer: Both variables likely increase in summer due to hot weather

A high correlation indicates association, not causation; a third variable (hot weather/summer) most plausibly explains both trends.

If you flip a fair coin 10 times and get heads all 10 times, what is the probability of getting heads on the 11th flip?

Answer: 0.5

Each coin flip is an independent event; past outcomes do not affect future ones, so the probability remains 0.5.

A company reports a 300% increase in profits. If profits were $10,000 last year, what are they now?

Answer: $40,000

A 300% increase means adding 300% of $10,000 (=$30,000) to the original, giving $10,000 + $30,000 = $40,000.

A chart shows that Country A has 2,000 doctors for 1 million people, and Country B has 1,000 doctors for 400,000 people. Which has more doctors per capita?

Answer: Country B

Country A: 2,000/1,000,000 = 0.002; Country B: 1,000/400,000 = 0.0025, so Country B has more doctors per capita.

An average (mean) is presented without a measure of variability. Why is this information incomplete for critical evaluation?

Answer: The mean alone cannot reveal how spread out the data are

Without variance or standard deviation, two datasets with the same mean could have very different distributions, making comparisons misleading.

A health agency reports that a vaccine is '95% effective.' A critic claims '5% still get sick, so it doesn't work well.' Which quantitative reasoning error does the critic make?

Answer: Misinterpreting relative effectiveness as absolute failure

95% effectiveness means the vaccine reduces disease risk by 95% compared to no vaccine; the critic ignores the baseline risk without vaccination.