STATS 10 flash cards
46 cards for Introduction to Statistical Reasoning, laid out week by week and timed around your exams. Free on iPhone and the web.
Exam dates
Unblank times your reviews around these. You can always set your own dates in the app.
- FinalWed, Mar 17, 2027A sample date until the Registrar posts the real one
The first 20 cards
Read the question, think of your answer, then open the card.
Week 1 · Kinds of variablesHow does a categorical variable differ from a quantitative one?Show the answerHide the answer
A categorical variable puts individuals into groups; a quantitative one records numbers you can sensibly average.
A zip code is a number but categorical: averaging zip codes means nothing.
Week 1 · Observational studies and experimentsWhat separates an experiment from an observational study?Show the answerHide the answer
In an experiment the researcher assigns the treatment. An observational study only records what people already do.
Week 1 · Observational studies and experimentsWhat is a confounding variable?Show the answerHide the answer
A variable tied to both the explanatory variable and the response, so their effects on the response can't be told apart.
Week 1 · Observational studies and experimentsWhy do experiments assign treatments at random?Show the answerHide the answer
Randomizing tends to balance other differences, known and unknown, across the groups, so a difference in outcomes can be credited to the treatment.
Week 2 · Center and spreadWhen does the median describe the center better than the mean?Show the answerHide the answer
When the distribution is skewed or has outliers, because the median barely moves with extreme values.
Household income is the usual example: a few huge incomes drag the mean up.
Week 2 · Center and spreadIn a right-skewed distribution, how do the mean and median usually compare?Show the answerHide the answer
The mean is larger: the long right tail pulls it up, while the median stays near the bulk of the data.
Week 2 · Center and spreadWhat are the mean and standard deviation of 2, 4, 4, 5, 10?Show the answerHide the answer
Mean 25/5 = 5. Squared deviations sum to 9 + 1 + 1 + 0 + 25 = 36, so s = √(36/4) = 3.
The sample standard deviation divides by n − 1, here 4, not n.
Week 2 · Center and spreadA data set has Q1 = 20 and Q3 = 32. Is 52 an outlier by the 1.5 × IQR rule?Show the answerHide the answer
Yes. IQR = 12, so the upper fence is 32 + 1.5 × 12 = 50, and 52 lies beyond it.
Week 2 · Center and spreadWhat does the standard deviation measure?Show the answerHide the answer
Roughly how far observations typically fall from the mean.
It is in the same units as the data, and it is 0 only when every value is the same.
Week 3 · Normal distributions and z-scoresWhat is a z-score?Show the answerHide the answer
How many standard deviations a value lies above or below the mean: z = (x − μ)/σ.
Week 3 · Normal distributions and z-scoresExam scores have mean 70 and standard deviation 8. What is the z-score of a score of 82?Show the answerHide the answer
z = (82 − 70)/8 = 1.5, so the score is 1.5 standard deviations above the mean.
Week 3 · Normal distributions and z-scoresWhat does the 68-95-99.7 rule say?Show the answerHide the answer
In a normal distribution, about 68% of values fall within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3.
Week 3 · Normal distributions and z-scoresHeights are normal with mean 64 inches and standard deviation 3. About what share are taller than 70 inches?Show the answerHide the answer
About 2.5%. 70 is 2 standard deviations above the mean, and half of the 5% outside ±2 lies above.
A normal table gives the more exact 2.3%.
Week 3 · Normal distributions and z-scoresAna scores 85 on a test with mean 75 and SD 5. Ben scores 90 on one with mean 80 and SD 10. Who did better relative to the class?Show the answerHide the answer
Ana. Her z-score is (85 − 75)/5 = 2, while Ben's is (90 − 80)/10 = 1.
Week 4 · Correlation and regressionWhat does the correlation r measure?Show the answerHide the answer
The direction and strength of the linear relationship between two quantitative variables, on a scale from −1 to 1.
Week 4 · Correlation and regressionIf r is close to 0, are the two variables unrelated?Show the answerHide the answer
Not necessarily. r only measures linear association; a strong curved pattern can still give r near 0.
Week 4 · Correlation and regressionThe line ŷ = 30 + 2.5x predicts exam score from hours studied. A student who studied 8 hours scored 55. What is the residual?Show the answerHide the answer
Predicted ŷ = 30 + 2.5 × 8 = 50, so the residual is 55 − 50 = 5.
A residual is observed minus predicted; a positive one means the point sits above the line.
Week 4 · Correlation and regressionIn ŷ = 30 + 2.5x, with x hours studied and ŷ the predicted score, what does the 2.5 mean?Show the answerHide the answer
Each extra hour of study goes with a predicted score 2.5 points higher, on average.
Week 4 · Correlation and regressionA regression has r = −0.6. What fraction of the variation in y does the line explain?Show the answerHide the answer
r² = (−0.6)² = 0.36, so 36%.
The sign of r doesn't matter for r²; the other 64% is left in the residuals.
Week 5 · Sampling methods and biasWhat is a simple random sample?Show the answerHide the answer
A sample chosen so that every possible group of n individuals has the same chance of being the one selected.
Week by week
The whole deck: 46 cards over 10 weeks. Every week is open from day one.
- 1Data and study design4 cards
- Kinds of variables 1
- Observational studies and experiments 3
- 2Describing data5 cards
- Center and spread 5
- 3The normal model5 cards
- Normal distributions and z-scores 5
- 4Correlation and regression5 cards
- Correlation and regression 5
- 5Sampling4 cards
- Sampling methods and bias 4
- 6Probability5 cards
- Probability rules 5
- 7Sampling distributions4 cards
- Sampling distributions 4
- 8Confidence intervals5 cards
- Confidence intervals 5
- 9Hypothesis tests5 cards
- Hypothesis tests 5
- 10Comparing groups4 cards
- Comparing two means 1
- Chi-square tests 3