Skill: descriptive-statistics

Descriptive Stats Practice

Summarize data with measures of center and spread, pick the right graph, and describe distributions with SOCS.

1 Practice

Type your answer and press Check answer (or Enter). A wrong answer earns a hint; a second miss earns a stronger hint; a third miss walks you through the full solution. Scores and streaks are session-only.

Score 0 · Streak 0 · Problem 0

Score counts first-try correct answers. Streak counts consecutive correct answers.

Problem

Enter integers or decimals. Round to two decimals where asked.

2 What you’ll practice

Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.

Mean

Add everything, divide by n.

Ex: 70, 74, 78, 80, 98 → 80

Median

Sort first, then take the middle.

Ex: 3, 7, 8, 12, 15, 18, 22 → 12

Standard deviation

Root-mean-square distance from the mean.

Ex: 4, 6, 8, 10, 12 → ≈3.16

IQR

Q3 − Q1 covers the middle 50%.

Ex: quartiles 5 and 11 → IQR 6

Skew direction

The mean chases the tail.

Ex: mean 62, median 71 → left skew

Graph choice

Categories → bars; measurements → histogram.

Ex: heights → histogram

SOCS

Shape first, then the matching pair.

Ex: salaries → median/IQR

3 Watch out for these

The mistakes students make most often on these problems.

Mean for skewed data

Incomes and house prices are right-skewed: the mean overstates “typical”. Report the median (and IQR) instead.

SD as “average deviation”

SD is the root-mean-square distance from the mean — the squaring penalizes far values more than |x − x̄| would.

Histogram for categories

Bars touch only for quantitative data. Favorite colors get a bar chart with separated bars.

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