← Back to the One-variable Data test
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: AP Statistics Unit 1 (2026-27) · Level: Grade 12 AP Statistics
Question 1 Categorical Data (2 points)
(a) Each student falls into a named group, so the variable is categorical. (b) 27/90 = 30%.
(a) categorical; (b) 30%
Scoring: 1 point each part.
Question 2 Mean, Median and Shape (2 points)
(a) Sum = 80, mean = 8. Median = (5 + 6)/2 = 5.5. (b) The distribution is skewed right (the 26 creates a long right tail), so the median, which is resistant, is more appropriate; the mean is pulled above the median.
(a) mean 8, median 5.5; (b) skewed right, use the median
Scoring: 1 point for both values, 1 point for shape with justification.
Question 3 Outliers and Boxplot (3 points)
(a) Min 22, Q1 = 27.5, median = 32, Q3 = 37, max 64. (b) IQR = 9.5, fences 13.25 and 51.25; 64 > 51.25 so 64 is an outlier. (c) The box runs from 27.5 to 37 with the median line at 32, the upper whisker ends at 41, and 64 is plotted as a separate point.
Five numbers 22, 27.5, 32, 37, 64; outlier: 64
Scoring: 1 point five-number summary, 1 point fences with conclusion, 1 point boxplot.
Question 4 Percentile and Shape (2 points)
(a) 13 players scored fewer than 4 goals: 13/20 = 65%. (b) Most values are small, and the tail extends to 11: skewed right.
(a) 65th percentile; (b) skewed right
Scoring: 1 point each part.
Question 5 Comparing Performances (2 points)
Running: z = (62.4 − 66.0)/3.0 = −1.20, which is 1.2 standard deviations faster than the mean. Jumping: z = (5.05 − 4.60)/0.30 = 1.50, which is 1.5 standard deviations farther than the mean. The jump is more unusual in the good direction.
Long jump (1.5 vs 1.2 standard deviations better than the mean)
Scoring: 1 point both z-scores, 1 point comparison that accounts for direction.
Question 6 Comparing Boxplots (3 points)
(a) The West store has the higher median, $3,000 versus $2,600. (b) IQR is 42 − 22 = 20 for West and 31 − 20 = 11 for East; the ranges are 50 and 33, so West sales vary more. (c) East has the more consistent sales because its IQR and range are smaller.
(a) West median is higher; (b) West has greater spread; (c) East is more consistent
Scoring: 1 point each part, answers must refer to context.
Question 7 Empirical Rule (2 points)
(a) 24 ± 2(5) gives 14 to 34 minutes. (b) 19 = 24 − 5 is one standard deviation below the mean; 68% lie within 1σ, so 32% lie outside, and 16% lie below.
(a) 14 to 34 minutes; (b) 16%
Scoring: 1 point each part.
Question 8 Normal Calculations (2 points)
(a) z = (75 − 63)/8.5 = 1.41; the area above is 0.0790. (b) The 20th percentile has z = −0.842, so x = 63 − 0.842(8.5) = 55.8 cm.
(a) ≈ 0.079; (b) ≈ 55.8 cm
Scoring: 1 point each part.
Question 9 Transforming Scores (2 points)
Adding 6 shifts the center but not the spread; multiplying by 1.25 changes both. New mean = 1.25(52 + 6) = 72.5, new median = 1.25(54 + 6) = 75.0, new SD = 1.25(9) = 11.25.
Mean 72.5, median 75, standard deviation 11.25
Scoring: 1 point for both centers, 1 point for standard deviation with reasoning.
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