Rucete ✏ AP Statistics In a Nutshell
1. Exploring One-Variable Data — Practice Questions 3
This set provides completely new practice problems on one-variable data, graphical displays, summary statistics, quartiles, z-scores, and distribution interpretation.
(Multiple Choice — Click to Reveal Answer)
1. Which variable is categorical?
(A) Age in years
(B) Number of pets
(C) Favorite snack
(D) Distance traveled
(E) Salary
Answer
(C) — Favorite snack is a category label. :contentReference[oaicite:0]{index=0}
2. Which variable is quantitative?
(A) Eye color
(B) Zip code category
(C) Number of goals scored
(D) Marital status
(E) Brand of phone
Answer
(C) — Number of goals scored is numerical. :contentReference[oaicite:1]{index=1}
3. Which graph is most appropriate for categorical data?
(A) Histogram
(B) Bar graph
(C) Boxplot
(D) Ogive
(E) Scatterplot
Answer
(B) — Bar graphs compare categories. :contentReference[oaicite:2]{index=2}
4. Which graph is most appropriate for many quantitative values?
(A) Pie chart
(B) Histogram
(C) Bar chart only
(D) Mosaic plot
(E) Circle graph
Answer
(B) — Histograms summarize quantitative distributions. :contentReference[oaicite:3]{index=3}
5. Relative frequency equals
(A) count + total
(B) count ÷ total
(C) total − count
(D) mean × count
(E) median ÷ total
Answer
(B) — Relative frequency is proportion of the total. :contentReference[oaicite:4]{index=4}
6. Which variable is continuous?
(A) Number of books
(B) Number of cars
(C) Height of a student
(D) Number of siblings
(E) Number of classes
Answer
(C) — Height is measured on a continuum. :contentReference[oaicite:5]{index=5}
7. Which variable is discrete?
(A) Weight
(B) Temperature
(C) Number of phone calls
(D) Time
(E) Distance
Answer
(C) — Number of phone calls is countable. :contentReference[oaicite:6]{index=6}
8. A distribution with two major peaks is called
(A) symmetric
(B) skewed
(C) bimodal
(D) uniform
(E) centered
Answer
(C) — Two clear peaks means bimodal. :contentReference[oaicite:7]{index=7}
9. A long tail to the right indicates
(A) left skew
(B) right skew
(C) symmetry
(D) no spread
(E) bimodal
Answer
(B) — Tail extending right means right-skewed. :contentReference[oaicite:8]{index=8}
10. A bell-shaped distribution is generally
(A) always skewed
(B) symmetric with center mound
(C) categorical
(D) flat only
(E) impossible
Answer
(B) — Bell-shaped distributions are symmetric with a central mound. :contentReference[oaicite:9]{index=9}
11. Which measure is resistant to outliers?
(A) Mean
(B) Median
(C) Range
(D) Standard deviation
(E) Variance
Answer
(B) — Median is less affected by extremes. :contentReference[oaicite:10]{index=10}
12. Mean of 4, 6, 8 is
(A) 5
(B) 6
(C) 7
(D) 8
(E) 18
Answer
(B) — (4+6+8)/3 = 6.
13. Median of 2, 5, 9, 12, 14 is
(A) 2
(B) 5
(C) 9
(D) 12
(E) 14
Answer
(C) — Middle ordered value is 9.
14. Range of 7, 10, 15, 20 is
(A) 10
(B) 13
(C) 15
(D) 20
(E) 27
Answer
(B) — 20 − 7 = 13.
15. If Q1 = 12 and Q3 = 20, then IQR =
(A) 8
(B) 10
(C) 12
(D) 20
(E) 32
Answer
(A) — 20 − 12 = 8.
16. If every value increases by 5, the mean
(A) decreases by 5
(B) unchanged
(C) increases by 5
(D) doubles
(E) becomes zero
Answer
(C) — Adding a constant shifts the mean equally. :contentReference[oaicite:11]{index=11}
17. If every value increases by 5, the range
(A) increases by 5
(B) unchanged
(C) decreases by 5
(D) doubles
(E) triples
Answer
(B) — Max and min both rise equally. :contentReference[oaicite:12]{index=12}
18. If all values are multiplied by 3, the standard deviation
(A) unchanged
(B) divided by 3
(C) multiplied by 3
(D) becomes zero
(E) increases by 1
Answer
(C) — Spread scales by the multiplier. :contentReference[oaicite:13]{index=13}
19. z-score tells how many
(A) categories exist
(B) quartiles exist
(C) SDs from mean
(D) ranges from min
(E) medians away
Answer
(C) — z-score measures distance from mean in SD units. :contentReference[oaicite:14]{index=14}
20. If x equals the mean, z =
(A) -1
(B) 0
(C) 1
(D) 2
(E) undefined
Answer
(B) — A value equal to mean has z = 0.
21. Which display retains exact individual values?
(A) Histogram
(B) Pie chart
(C) Stemplot
(D) Bar graph
(E) Boxplot
Answer
(C) — Stemplots preserve original values. :contentReference[oaicite:15]{index=15}
22. Which is an unusual feature of a distribution?
(A) Gap
(B) Axis title
(C) Gridline
(D) Label size
(E) Tick mark
Answer
(A) — Gaps are important unusual features. :contentReference[oaicite:16]{index=16}
23. Percentile rank of a value means percent of data
(A) above it only
(B) at or below it
(C) exactly equal to it
(D) outside range
(E) above median only
Answer
(B) — Standard percentile definition. :contentReference[oaicite:17]{index=17}
24. Which is true of real data?
(A) Always perfectly symmetric
(B) Often approximately shaped
(C) Never has outliers
(D) Mean always equals median
(E) Always uniform
Answer
(B) — Real data are usually approximate, not perfect. :contentReference[oaicite:18]{index=18}
25. Which statistic uses only the middle 50% spread?
(A) Range
(B) Mean
(C) IQR
(D) Maximum
(E) Count
Answer
(C) — IQR = Q3 − Q1. :contentReference[oaicite:19]{index=19}
26. Mean = 40, SD = 5. Find z for x = 50.
(A) 1
(B) 2
(C) -2
(D) 10
(E) 45
Answer
(B) — (50−40)/5 = 2.
27. Mean = 70, SD = 8. Find z for x = 62.
(A) -1
(B) 1
(C) -2
(D) 2
(E) 8
Answer
(A) — (62−70)/8 = -1.
28. Mean = 25, SD = 4. Raw score for z = 2 is
(A) 17
(B) 21
(C) 29
(D) 33
(E) 50
Answer
(D) — 25 + 2(4) = 33.
29. Q1 = 6, Q3 = 14. Upper outlier fence is
(A) 20
(B) 24
(C) 26
(D) 14
(E) 8
Answer
(C) — IQR=8, upper fence = 14 + 1.5(8)=26.
30. Q1 = 6, Q3 = 14. Lower outlier fence is
(A) -6
(B) 0
(C) 6
(D) 8
(E) 12
Answer
(A) — 6 − 12 = -6.
31. If 75% are at or below x, then percent above x is
(A) 15%
(B) 20%
(C) 25%
(D) 50%
(E) 75%
Answer
(C) — Remaining proportion is 25%.
32. Which center is usually better for right-skewed income data?
(A) Mean
(B) Median
(C) Range
(D) Variance
(E) Maximum
Answer
(B) — Median resists high outliers.
33. If all values are identical, SD equals
(A) 0
(B) 1
(C) mean
(D) range
(E) undefined
Answer
(A) — No variability means zero SD.
34. Which cumulative plot shape suggests right skew?
(A) Slow then steep then slow
(B) Steep first then flattening later
(C) Perfect straight line only
(D) Horizontal only
(E) Downward slope
Answer
(B) — Right-skewed data rise quickly early then slow later. :contentReference[oaicite:20]{index=20}
35. Which cumulative plot shape suggests left skew?
(A) Steep first then slow
(B) Slow first then steep later
(C) Horizontal only
(D) Negative slope
(E) Constant zero
Answer
(B) — Left-skewed data rise slowly then steeply. :contentReference[oaicite:21]{index=21}
36. Find the mean of 3, 6, 9, 12.
Answer
7.5 — Sum 30 divided by 4.
37. Find the median of 1, 4, 7, 10.
Answer
5.5 — Average of middle two values.
38. Find the range of 14, 18, 25, 30.
Answer
16 — 30 − 14 = 16.
39. Ordered data: 2,4,6,8,10. Find Q1.
Answer
3 — Median of lower half (2,4).
40. Ordered data: 2,4,6,8,10. Find Q3.
Answer
9 — Median of upper half (8,10).
41. Using Questions 39 and 40, find IQR.
Answer
6 — 9 − 3 = 6.
42. Mean = 90, SD = 6. Find z-score of 78.
Answer
-2 — (78−90)/6 = -2.
43. Mean = 90, SD = 6. Find raw score for z = 1.
Answer
96 — 90 + 1(6).
44. If 16 of 20 scores are at or below 88, what percentile is 88?
Answer
80th percentile — 16/20 = 0.80.
45. If every value decreases by 3, how much does median change?
Answer
Decreases by 3 — Median shifts with all values.
46. If every value is doubled, how does range change?
Answer
Doubles — Range scales by multiplier.
47. If z = 0 and mean = 55, what is x?
Answer
55 — z = 0 corresponds to the mean.
48. A value is 1.5 SD below mean. What is z?
Answer
-1.5 — Below mean gives negative z.
49. If Q1 = 18 and Q3 = 30, find IQR.
Answer
12 — 30 − 18 = 12.
50. If cumulative relative frequency at x = 40 is 0.65, what percent are above 40?
Answer
35% — 1 − 0.65 = 0.35.