Rucete ✏ AP Statistics In a Nutshell
1. Exploring One-Variable Data — Practice Questions 2
This chapter introduces new practice problems on categorical and quantitative data, displays, center, spread, quartiles, and z-scores.
(Multiple Choice — Click to Reveal Answer)
1. Which variable is categorical?
(A) Number of pets owned
(B) Daily temperature
(C) Shoe brand
(D) Height of a student
(E) Hours slept last night
Answer
(C) — Shoe brand is a label/category.
2. Which variable is quantitative?
(A) Favorite color
(B) Blood type
(C) Number of absences
(D) Political party
(E) Car model
Answer
(C) — Number of absences is numerical.
3. Which display is best for categorical data?
(A) Histogram
(B) Bar graph
(C) Boxplot
(D) Stemplot
(E) Dotplot of decimals
Answer
(B) — Bar graphs are standard for categorical variables.
4. Which display is best for many quantitative observations?
(A) Pie chart
(B) Histogram
(C) Bar graph
(D) Mosaic plot
(E) Circle graph
Answer
(B) — Histograms are useful for larger quantitative data sets.
5. Relative frequency means
(A) largest value
(B) count divided by total
(C) median only
(D) mode only
(E) sum of values
Answer
(B) — Relative frequency = proportion of the total.
6. In a pie chart, all sectors should total
(A) 50%
(B) 90%
(C) 100%
(D) sample size
(E) median
Answer
(C) — Pie charts represent a whole.
7. Which variable is continuous?
(A) Number of siblings
(B) Number of goals scored
(C) Weight of luggage
(D) Number of cars owned
(E) Number of books
Answer
(C) — Weight can take many measured values.
8. Which variable is discrete?
(A) Height
(B) Time
(C) Number of classes taken
(D) Temperature
(E) Distance
Answer
(C) — Number of classes is countable.
9. A distribution with one clear peak is called
(A) symmetric
(B) unimodal
(C) bimodal
(D) skewed
(E) uniform
Answer
(B) — One major peak means unimodal.
10. A distribution with a long left tail is
(A) skewed left
(B) skewed right
(C) uniform
(D) bimodal
(E) symmetric
Answer
(A) — Tail toward lower values indicates left skew.
11. Which measure is resistant to outliers?
(A) Mean
(B) Median
(C) Range
(D) Variance
(E) Standard deviation
Answer
(B) — Median is resistant to extreme values.
12. The mean of 2, 4, 6 is
(A) 3
(B) 4
(C) 5
(D) 6
(E) 12
Answer
(B) — (2+4+6)/3 = 4.
13. The median of 1, 5, 8, 10, 12 is
(A) 1
(B) 5
(C) 8
(D) 10
(E) 12
Answer
(C) — Middle ordered value is 8.
14. Range equals
(A) Q3 − Q1
(B) max − min
(C) mean − median
(D) variance squared
(E) mode − median
Answer
(B) — Range is largest minus smallest.
15. IQR equals
(A) max − min
(B) Q1 − Q3
(C) Q3 − Q1
(D) mean + SD
(E) median / 2
Answer
(C) — IQR measures middle 50% spread.
16. If Q1 = 10 and Q3 = 18, then IQR is
(A) 8
(B) 10
(C) 18
(D) 28
(E) 4
Answer
(A) — 18 − 10 = 8.
17. If every value increases by 4, the mean
(A) decreases by 4
(B) unchanged
(C) increases by 4
(D) doubles
(E) becomes zero
Answer
(C) — Adding a constant shifts the mean equally.
18. If every value increases by 4, the range
(A) increases by 4
(B) decreases by 4
(C) unchanged
(D) doubles
(E) becomes zero
Answer
(C) — Spread between max and min stays the same.
19. If all values are multiplied by 2, the standard deviation
(A) halves
(B) unchanged
(C) doubles
(D) becomes zero
(E) increases by 1
Answer
(C) — SD scales by the multiplier.
20. z-score measures
(A) category type
(B) percent of pie chart
(C) number of SDs from mean
(D) range only
(E) quartile only
Answer
(C) — z-score expresses distance from mean in SD units.
21. If x = mean, then z =
(A) -1
(B) 0
(C) 1
(D) 2
(E) undefined
Answer
(B) — A value equal to mean has zero distance.
22. Which is an unusual feature?
(A) Gap
(B) Axis label
(C) Percent sign
(D) Scale mark
(E) Title
Answer
(A) — Gaps are unusual features in distributions.
23. Which graph preserves exact data values?
(A) Histogram
(B) Pie chart
(C) Stemplot
(D) Bar graph
(E) Density curve only
Answer
(C) — Stemplots show individual values.
24. Which statement is true about real data?
(A) Always perfectly symmetric
(B) Usually approximately shaped
(C) Never have outliers
(D) Mean always equals median
(E) Always bimodal
Answer
(B) — Real distributions are often approximate.
25. Percentile rank of a value means percent of data
(A) above it only
(B) equal to it only
(C) at or below it
(D) outside IQR
(E) within one SD
Answer
(C) — Standard percentile definition.
26. Data set: 3, 7, 9, 11, 20. Which measure changes most if 20 becomes 50?
(A) Median
(B) Mean
(C) Q1
(D) Q3
(E) Position of middle value
Answer
(B) — Mean is sensitive to extreme values.
27. If a histogram is flat across equal-width bins, it is approximately
(A) skewed right
(B) skewed left
(C) uniform
(D) bimodal
(E) bell-shaped
Answer
(C) — Equal heights across bins suggest uniformity.
28. Which statistic best describes center of a skewed distribution with outliers?
(A) Mean
(B) Median
(C) Range
(D) Variance
(E) Maximum
Answer
(B) — Median is more robust for skewed data.
29. A value with z = -2 lies
(A) 2 SD above mean
(B) 2 SD below mean
(C) at the median only
(D) at Q1
(E) impossible
Answer
(B) — Negative means below mean.
30. If mean = 50 and SD = 5, then x = 60 has z =
(A) 1
(B) 2
(C) -2
(D) 10
(E) 12
Answer
(B) — (60−50)/5 = 2.
31. If mean = 80 and SD = 4, then x = 72 has z =
(A) -2
(B) -1
(C) 1
(D) 2
(E) 8
Answer
(A) — (72−80)/4 = -2.
32. If Q1 = 5 and IQR = 6, then Q3 =
(A) -1
(B) 1
(C) 6
(D) 11
(E) 30
Answer
(D) — Q3 = 5 + 6 = 11.
33. Upper outlier fence when Q1=5, Q3=11 is
(A) 14
(B) 20
(C) 30
(D) 11
(E) 9
Answer
(B) — IQR=6, upper fence = 11 + 1.5(6)=20.
34. Lower outlier fence when Q1=5, Q3=11 is
(A) -4
(B) 0
(C) 5
(D) 9
(E) 20
Answer
(A) — 5 − 9 = -4.
35. If 80% are at or below x on an ogive, then 20% are
(A) below zero
(B) above x
(C) equal to x exactly
(D) in Q1 only
(E) impossible to know
Answer
(B) — Remaining proportion is above x.
36. Find the mean of 5, 10, 15, 20.
Answer
12.5 — Sum 50 divided by 4.
37. Find the median of 2, 4, 6, 8.
Answer
5 — Average of middle two values: (4+6)/2.
38. Find the range of 9, 12, 17, 25.
Answer
16 — 25 − 9 = 16.
39. Ordered data: 1,3,5,7,9. Find Q1.
Answer
2 — Lower half is 1,3 so median is 2.
40. Ordered data: 1,3,5,7,9. Find Q3.
Answer
8 — Upper half is 7,9 so median is 8.
41. Using Questions 39 and 40, find IQR.
Answer
6 — 8 − 2 = 6.
42. Mean = 30, SD = 10. Find z-score of 50.
Answer
2 — (50−30)/10 = 2.
43. Mean = 30, SD = 10. Find raw score when z = -1.
Answer
20 — 30 + (-1)(10) = 20.
44. If 18 of 24 students scored at or below 70, what percentile is 70?
Answer
75th percentile — 18/24 = 0.75.
45. If every value increases by 9, how much does median increase?
Answer
9 — Median shifts by same constant.
46. If every value is tripled, how does range change?
Answer
Triples — Range scales by multiplier.
47. If mean = 100 and z = 0, what is x?
Answer
100 — z = 0 means x equals mean.
48. A value is 3 SD above mean. What is its z-score?
Answer
3 — Direct definition of z-score.
49. If Q1=14 and Q3=22, what is IQR?
Answer
8 — 22 − 14 = 8.
50. If cumulative relative frequency at x=12 is 0.60, what percent are above 12?
Answer
40% — 1.00 − 0.60 = 0.40.