Daily 5 - Feb 2

Class Performance

Students: 106 | Mean: 3.74 | Median: 4 | SD: 0.79

Scores ranged from 2 to 5 out of 5 points.

Correct Answer

E(Y) = Σ p_j y_j — The expected value is the sum of each possible value multiplied by its probability.

Common Errors

Missing summation notation — Writing “p·y” without the Σ symbol. The formula requires summation over all values.
Wrong operator — Using multiplication (×) instead of summation (Σ) between terms.
Conceptual only — Describing “weighted average” without writing the mathematical formula requested.

Correct Answer

Var(Y) = Σ p_j(y_j − μ_y)² — The variance is the sum of probability-weighted squared deviations from the mean.

Common Errors

Wrote expected value instead — Many students repeated the E(Y) formula. Variance measures spread, not center.
Missing squared term — Writing (y_j − μ) without squaring. The squared term is essential to variance.
Wrote sample mean formula — Ȳ = (1/n)Σy_i is sample mean, not variance.
Conceptual description only — “Average distance from mean” is incomplete; variance uses squared deviations.

Correct Answer

7% — The overall gender wage gap documented by the Uber study authors and reported in the Freakonomics podcast.

Common Errors

Wrong percentages — Common incorrect answers included 8%, 18%, 19%, 25%, 30%, 35%. The exact figure was 7%.
Confusing with other statistics — Some wrote wage gaps from other studies or contexts.
Left blank — This was a recall question from the podcast material.

Correct Answer

The code keeps/restricts to individuals where age is between 23 and 62 — selecting working-age adults for the “defining a career” analysis.

Common Errors

Used prohibited word “filter” — The question specifically asked to explain without using that word. Use “keeps,” “restricts,” or “selects.”
Vague about age bounds — Saying “restricts by age” without specifying the exact range (23-62).
Wrong age bounds — Some wrote 26 or 40 as the upper bound instead of 62.

Correct Answer

does not — The key idea behind random sampling is that one draw from the population does not depend on another (independence).

Common Errors

Very few errors — This was the best-performing question with near-perfect scores.
Writing “does” instead of “does not” — Random sampling requires observations to be independent.

Strengths: Expected value formula, random sampling independence concept, understanding of wage gap research.

Review:

Variance formula — Var(Y) = Σp_j(y_j − μ)² requires the squared deviation term
Uber wage gap = 7% — From the Freakonomics podcast assigned listening
Code interpretation — Be precise about what code does (ages 23-62), and follow question instructions (don’t use prohibited words)