What's on the Test?
Test 3 covers two major topic areas: Statistics & Distributions and Exponential & Linear Growth. You'll need to interpret data, calculate descriptive statistics, reason about normal distributions, and apply growth models.
The test has 25 questions — a mix of multiple-choice and fill-in-the-blank — and includes questions that ask you to reason without calculating, so be sure to understand the concepts, not just the formulas.
💡 Study Hints
- 50th percentile = median. The median splits the data exactly in half — the same thing the 50th percentile does.
- Range rule of thumb: Estimated std. deviation ≈ Range ÷ 4. It works best when data is spread evenly.
- 68–95–99.7 rule: In a normal distribution, ~68% of data falls within 1 std. dev., ~95% within 2, ~99.7% within 3.
- Doubling time formula (approximate): Tdouble ≈ 70 ÷ growth rate %. Exact: T = log(2) ÷ log(1 + r).
- Skewness clue: If mean > median, the distribution is right-skewed (pulled by high outliers). If mean < median, it's left-skewed.
- Linear vs. exponential growth: Linear grows by a fixed amount each period; exponential grows by a fixed percentage.
- Median is best for income data because a few very high earners can distort the mean significantly.
- Z-score sign: Negative z-scores are below the mean, positive are above. z = (value − mean) ÷ std. dev.
Maria scored in the 25th percentile on a standardized exam. Which of the following best describes her score?
Without calculating, determine whether the following statement is true or false.
103.45 is between 1,000 and 10,000.
Find the mean, median, and mode for the following set of numbers:
12 18 7 25 18 9 31 14
A study of household net worth in a U.S. city found:
Mean net worth = $480,000 · Median net worth = $120,000
Which best describes this distribution, and why?
The weights of apples from an orchard are normally distributed with a mean = 150 g and std. dev. = 10 g.
What percentage of apples weigh less than 130 g?
Which z-score correctly describes: "a data value 2.3 standard deviations below the mean"?
A city's population of 50,000 is growing at 7% per year. Using the approximate doubling time formula (Rule of 70), about how many years will it take for the population to double?
A tree farm plants 200 new trees every month, regardless of how many trees exist. A second farm doubles its tree count every 6 months starting from 200 trees.
Which statement is true?
A researcher wants to report a "typical" salary for employees at a company where most workers earn between $40,000–$60,000, but the CEO earns $5,000,000. Which measure of center is most appropriate and why?
A radioactive substance has a current mass of 800 g and a half-life of 10 years. How much will remain after 30 years?