Student exam scores

Final mathematics exam scores for 400 grade-11 students in a fictional school district, Al Waha Learning District, with weekly study hours, attendance, the previous year's score, school type and whether the student received after-school tutoring. Tutoring was offered mainly to students who had struggled, so the raw comparison of tutored vs untutored students is misleading — a good dataset for correlation vs causation, confounding and multiple regression with a bounded outcome.

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Rows: 400
Columns: 7
One row is: one student
Version: v1

Data dictionary

Column	Type	Unit	Summary	Description
`student_id` Student	id			Anonymous student code.
`school_type` School type	category		3 levels: Public, Private, International	Type of school.
`prior_score` Prior score	integer	points	mean 69.38, median 69, SD 12.62, range 29–100	Previous year's final mathematics score (0–100).
`study_hours_week` Study hours	number	hours/week	mean 4.814, median 4.3, SD 2.611, range 0.5–17.2	Self-reported average independent study hours per week.
`attendance_pct` Attendance	number	%	mean 91.57, median 92.95, SD 6.073, range 60.8–99.8	Percentage of classes attended this year.
`tutoring` Tutoring	boolean		2 levels	True if the student attended the after-school tutoring programme.
`exam_score` Exam score	integer	points	mean 70.86, median 71, SD 11.14, range 39–100	Final exam score (0–100).

What it is good for

Compute and interpret correlations between study habits and scores.
Show that a raw comparison understates (or even reverses) the tutoring effect because tutored students started lower.
Fit a multiple regression controlling for prior score and interpret the tutoring coefficient.
Discuss bounded outcomes (ceiling at 100) and the limits of observational data.

Methods: correlation, scatter plot matrix, two-sample t-test, multiple regression, confounding, ANCOVA.

Data quality notes

Tutoring is confounded with prior score: tutored students had much lower prior scores.
Exam scores are bounded at 0 and 100; a few students hit the ceiling.
Study hours are self-reported.
No missing values.

Provenance and licence

Prior score ~ Normal(68, 13) bounded to 20–100 (school-type shifts). Study hours are gamma, rising slightly with prior score; attendance is beta-distributed (median ≈92%). Tutoring is assigned with probability logistic(−0.9 − 0.09·(prior − 68)), so weaker students are much more likely to be tutored. Exam = 22 + 0.6·prior + 1.0·hours + 0.25·(attendance − 90) + 4·tutoring + school effect + Normal(0, 7), rounded and clamped to 0–100 (a few scores hit the 100 ceiling).

Synthetic data · CC0-1.0 (synthetic data generated by Statistics Quest) · generated deterministically (seed 20241022). It does not describe real people or organisations; any resemblance is coincidental.

Preview

Dataset

Student exam scores

400 rows · one row = one student · synthetic data

About this dataset Open in the lab

Student	School type	Prior score (points)	Study hours (hours/week)	Attendance (%)	Tutoring	Exam score (points)
ST001	Private	76	5.2	89	false	66
ST002	Public	75	4.1	94.4	false	73
ST003	Private	83	2	86.1	true	86
ST004	Public	81	8.6	88.2	false	81
ST005	Public	70	4.9	85.2	false	74
ST006	Public	80	1.7	93.5	false	83
ST007	Public	92	3.7	91.9	false	75
ST008	Private	62	5.2	85.8	false	68
ST009	Private	68	1.6	86.6	false	59
ST010	Private	87	7.2	93.3	false	100
ST011	Private	63	2.4	93.1	false	72
ST012	Public	74	3.8	87.8	false	74

Used in

Variables and observations · Statistical Thinking
Confounding and causation · Statistical Thinking
z-scores and relative standing · Describing Data
Shape: skewness and kurtosis · Describing Data
Histograms · Visualising and Exploring Data
ECDFs and Q-Q plots · Visualising and Exploring Data
Correlation is not causation · Correlation and Regression
Principal component analysis · Advanced Foundations
Causal inference: potential outcomes and causal diagrams · Advanced Foundations
Does tutoring raise exam scores? · Case