AP Statistics Quiz: Graphical Representations Of Summary Statistics

What this quiz covers

This quiz focuses on Graphical Representations Of Summary Statistics, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. The range is $25-5=20$ dollars.
2. The IQR is $120-1=119$ dollars.
3. The box extends from $Q_1=5$ to $Q_3=25$, with a median line at 12. (correct answer)
4. The right whisker must extend to 120 dollars because it is the maximum donation.
5. Because the maximum is large, the median must be greater than $Q_3$.

Explanation: This question tests understanding of modified boxplot construction with the 1.5·IQR rule. The box always extends from Q₁ to Q₃ with the median line inside. Given Q₁ = 5, Q₃ = 25, and median = 12, the box extends from 5 to 25 dollars with the median at 12 dollars, making choice C correct. Choice A incorrectly identifies the IQR as the range; IQR = Q₃ - Q₁ = 25 - 5 = 20 dollars. Choice B incorrectly calculates IQR using max - min. Choice D is incorrect because with IQR = 20, the upper fence = 25 + 1.5(20) = 55, so 120 would be plotted as an outlier point, not connected by the whisker. Choice E makes a logical error; the median cannot be greater than Q₃ by definition, as Q₃ represents the 75th percentile while the median is the 50th percentile.

Question 2

1. The median is at 6 absences.
2. The left whisker extends from 1 down to 0 absences. (correct answer)
3. The interquartile range is $15-0=15$ absences.
4. The box extends from 0 to 15 absences.
5. The maximum value (15) must be shown as an outlier point, not as a whisker endpoint.

Explanation: This question tests understanding of whisker placement in boxplots. The left whisker should extend from Q1 down to the minimum value, which means from 1 down to 0 absences, making option B correct. Option A incorrectly places the median at Q3's value (6) instead of 3. Option C calculates a range (max - min = 15 - 0 = 15) rather than the IQR (Q3 - Q1 = 6 - 1 = 5). Option D incorrectly extends the box from min to max (0 to 15) instead of Q1 to Q3 (1 to 6). Option E misapplies outlier rules when the problem explicitly states no outliers are marked. Key concept: whiskers connect the box edges (Q1 and Q3) to the minimum and maximum values, not to each other.

Question 3

1. The right whisker extends from 88 to 97 $^\circ$F. (correct answer)
2. The median is at 88 $^\circ$F.
3. The IQR is $97-71=26$ $^\circ$F.
4. The box extends from 71 to 97 $^\circ$F.
5. The left whisker ends at 78 $^\circ$F because $Q_1$ is the minimum.

Explanation: This question assesses understanding of whisker placement in temperature data. The right whisker extends from Q3 to the maximum value, which means from 88 to 97°F, making option A correct. Option B incorrectly places the median at Q3's position (88) when it should be at 83°F. Option C calculates max - min (97 - 71 = 26) and calls it the IQR, but the IQR should be Q3 - Q1 (88 - 78 = 10). Option D incorrectly extends the box from min to max (71 to 97) instead of Q1 to Q3 (78 to 88). Option E misunderstands the five-number summary; Q1 (78) is not the minimum value (71). Remember: whiskers show the data range beyond the quartiles, extending from the box edges to the extreme values.

Question 4

1. The median line is drawn at 11 hours.
2. The interquartile range is $26-0.5=25.5$ hours.
3. The box extends from 3 to 11 hours. (correct answer)
4. The left whisker ends at 3 hours.
5. The maximum (26) must be shown as an outlier point, so the right whisker ends at 11 hours.

Explanation: This question tests identification of the box portion in a boxplot with streaming data. The box extends from Q1 to Q3, which is from 3 to 11 hours, making option C correct. Option A incorrectly places the median at Q3's value (11) instead of 6.5 hours. Option B calculates max - min (26 - 0.5 = 25.5) rather than the IQR, which is Q3 - Q1 (11 - 3 = 8). Option D states a fact about the whisker endpoint but doesn't identify the distinguishing feature of the box. Option E introduces outlier rules that don't apply since the problem explicitly states no outliers are marked. Key concept: the box in a boxplot represents the interquartile range, containing the middle 50% of observations between Q1 and Q3.

Question 5

1. The box extends from 6 to 33 pounds.
2. The IQR is $33-6=27$ pounds.
3. The median is located at 13 pounds, between $Q_1$ and $Q_3$. (correct answer)
4. The right whisker ends at 18 pounds.
5. The range is $18-10=8$ pounds.

Explanation: This question tests recognition of correct boxplot features from summary statistics. Given the five-number summary (min=6, Q1=10, median=13, Q3=18, max=33), we need to identify the correct statement. The box extends from Q1 to Q3 (10 to 18 pounds), not 6 to 33. The IQR is Q3-Q1 = 18-10 = 8 pounds, not 27. The median at 13 pounds is correctly positioned between Q1 (10) and Q3 (18), making choice C correct. The right whisker extends from Q3 to the maximum, ending at 33 pounds, not 18. The range is max-min = 33-6 = 27 pounds, not 8. When interpreting boxplots, the median line must always fall within the box, as it represents a value between the 25th and 75th percentiles of the distribution.

Question 6

1. The range is $84-62=22$ points.
2. The box extends from 62 to 84 points. (correct answer)
3. The median line is drawn at 84 points.
4. The left whisker ends at 62 points.
5. Any score above 98 must be shown as an outlier on the boxplot.

Explanation: This question tests recognition of boxplot components from summary statistics. Given the five-number summary (min=40, Q1=62, median=70, Q3=84, max=98), we need to identify which statement correctly describes a boxplot feature. The box in a boxplot always extends from Q1 to Q3, which here is from 62 to 84 points, making choice B correct. The range is maximum minus minimum (98-40 = 58 points), not 22. The median line should be at 70 points, not 84. The left whisker extends from the minimum (40) to Q1 (62), not ending at 62. Without specific outlier rules given, we cannot determine if 98 would be an outlier. Remember that the box represents the interquartile range and contains the middle 50% of the data.

Question 7

1. The median is at 4 because $Q_3=4$.
2. The box extends from 1 to 4 with a median line at 2. (correct answer)
3. The range is $4-1=3$ books.
4. The whiskers extend from 1 to 4, and the box extends from 0 to 12.
5. The maximum value 12 must be plotted as an outlier point beyond the whisker.

Explanation: This question assesses understanding of boxplot construction from summary statistics. The box extends from Q₁ (1) to Q₃ (4), with the median line at 2 positioned inside this box. The whiskers extend from the box edges to the minimum (0) and maximum (12) values. Choice B correctly identifies that the box extends from 1 to 4 with a median line at 2. Common misconceptions in the distractors include: confusing Q₃ with the median, calculating range instead of identifying boxplot features (range is 12-0=12, not 3), reversing box and whisker positions, and assuming extreme values must be outliers. Remember that in a standard boxplot from a five-number summary, all five values are incorporated into the plot structure.

Question 8

1. The median is drawn at 41.
2. The box extends from 29 to 41, and the median line is at 34. (correct answer)
3. The interquartile range is $49-11=38$.
4. The left whisker ends at 29 because $Q_1$ is the minimum.
5. The right whisker ends at 34 because the median is the largest value shown by a whisker.

Explanation: This question tests comprehensive boxplot interpretation with quiz scores. The box extends from Q1 to Q3 (29 to 41), and the median line is drawn at 34, making option B correct. Option A incorrectly places the median at Q3's position (41) instead of 34. Option C calculates the range (max - min = 49 - 11 = 38) rather than the IQR, which is Q3 - Q1 (41 - 29 = 12). Option D incorrectly claims Q1 equals the minimum; Q1 is 29 but the minimum is 11. Option E makes no sense as whiskers extend to extreme values, not to the median. Remember: reading a boxplot requires identifying five key values - the minimum, Q1, median, Q3, and maximum - each serving a specific role in the display.

Question 9

1. The median is drawn at 9 minutes.
2. The range is $9-4=5$ minutes.
3. The box extends from 4 to 9 minutes. (correct answer)
4. The left whisker ends at 4 minutes.
5. The maximum (20) must be plotted as an outlier point rather than as the whisker endpoint.

Explanation: This question tests recognition of the box component in a boxplot. The box extends from Q1 to Q3, which is from 4 to 9 minutes, making option C correct. Option A incorrectly places the median at Q3's value (9) instead of 6. Option B calculates Q3 - Q1 (9 - 4 = 5) but mislabels it as the range rather than the IQR; the range would be max - min = 20 - 2 = 18. Option D correctly identifies where the left whisker ends but this isn't the distinguishing feature asked for. Option E introduces outlier considerations that aren't applicable since the problem states no outliers are marked. Key insight: the box in a boxplot always spans from the first quartile to the third quartile, representing where the middle half of the data falls.

Question 10

1. The box extends from 2.0 to 7.5, and the whiskers extend from 3.5 to 5.0.
2. The median line is located at 4.2 within a box from 3.5 to 5.0. (correct answer)
3. The interquartile range is $7.5-2.0=5.5$ miles.
4. Because the maximum is 7.5, 7.5 must be an outlier and not part of the whisker.
5. The left whisker extends from 5.0 down to 3.5.

Explanation: This question tests recognition of correct boxplot features from given summary statistics. In a boxplot, the box spans from Q₁ (3.5) to Q₃ (5.0), with the median line drawn at 4.2 within this box. The whiskers extend from the box to the minimum (2.0) and maximum (7.5) values. Choice B correctly states that the median line is at 4.2 within a box from 3.5 to 5.0. The distractors reveal common misunderstandings: the box doesn't extend to the extremes, the IQR is 5.0-3.5=1.5 miles (not 5.5), values in a five-number summary are not outliers, and whiskers extend outward from the box (not between quartiles). A key principle: the box always contains the middle 50% of the data.

Question 11

1. The IQR is $44-18=26$ minutes. (correct answer)
2. The median is at 18 minutes.
3. The left whisker ends at 44 minutes.
4. The box extends from 9 to 90 minutes.
5. The range is $44-18=26$ minutes.

Explanation: This question requires calculating boxplot features from given summary statistics. With the five-number summary (min=9, Q1=18, median=27, Q3=44, max=90), we can determine each component. The IQR equals Q3-Q1 = 44-18 = 26 minutes, which matches choice A. The median is at 27 minutes, not 18. The left whisker extends from the minimum (9) to Q1 (18), not ending at 44. The box extends from Q1 to Q3 (18 to 44), not from minimum to maximum. The range is max-min = 90-9 = 81 minutes, not 26. Remember that IQR measures the spread of the middle 50% of data and is represented by the length of the box in a boxplot.

Question 12

1. The left whisker has length $30-18=12$ packages. (correct answer)
2. The box has length $60-18=42$ packages.
3. The median is at 55 packages.
4. The right whisker ends at 55 packages.
5. The IQR equals $41-30=11$ packages.

Explanation: This question requires identifying correct boxplot features from given summary statistics. With the five-number summary (min=18, Q1=30, median=41, Q3=55, max=60), we can determine each boxplot component. The left whisker extends from the minimum (18) to Q1 (30), giving it a length of 30-18 = 12 packages, which matches choice A. The box itself extends from Q1 to Q3 (30 to 55), not from the minimum to maximum. The median line is at 41 packages, not 55. The right whisker extends from Q3 (55) to the maximum (60). The IQR equals Q3-Q1 = 55-30 = 25 packages, not 11. When reading boxplots, remember that whiskers connect the box to the extreme values, while the box itself spans only the middle 50% of the data.

Question 13

1. The median line is drawn at 18.
2. The right whisker extends from 18 to 29. (correct answer)
3. The IQR equals $29-8=21$.
4. The box extends from 8 to 29.
5. The left whisker extends from 8 to 14.

Explanation: This question evaluates knowledge of summary statistics representations, particularly ensuring boxplot features match the data. The right whisker extends from Q3 (18 thousand dollars) to the max (29), as described in choice B, which is consistent. The box is from Q1 (11) to Q3 (18), with median at 14, and left whisker from min (8) to Q1. Distractors like choice C confuse IQR (7) with range (21), and choice E extends the left whisker to the median instead of Q1. A mini-lesson on reading boxplots: focus on the five-number summary to understand center (median), spread (IQR and range), and shape (whisker asymmetry), which here shows a longer right whisker suggesting right-skewed prices.

Question 14

1. The box extends from 12 to 58 minutes.
2. The left whisker extends from 12 to 20 minutes. (correct answer)
3. The median is located at 35 minutes.
4. The interquartile range is 46 minutes.
5. The right whisker extends from 35 to 58 minutes.

Explanation: This question assesses the skill of interpreting graphical representations of summary statistics, particularly boxplots constructed from a five-number summary. In a standard boxplot without outliers, the box spans from the first quartile (Q1 = 20 minutes) to the third quartile (Q3 = 35 minutes), with the median line at 28 minutes, while the left whisker extends from the minimum (12 minutes) to Q1 (20 minutes) and the right whisker from Q3 to the maximum (58 minutes). Choice B correctly describes the left whisker extending from 12 to 20 minutes, which matches the summary statistics. A common distractor, like choice A, mistakenly describes the box as spanning the entire range from min to max, while choice D confuses the interquartile range (IQR = Q3 - Q1 = 15 minutes) with the full range. To read a boxplot effectively, identify the five key points: min, Q1, median, Q3, and max, which divide the data into quarters and highlight the distribution's spread and central tendency. Understanding these features helps in recognizing skewness, such as the longer right whisker here indicating potential right-skewness.

Question 15

1. The right whisker extends from 4 to 15 books. (correct answer)
2. The left whisker extends from 0 to 2 books.
3. The box extends from 0 to 15 books.
4. The IQR is $15-0=15$ books.
5. The median is at $Q_1=1$ book.

Explanation: This question assesses understanding of summary statistics through boxplots, emphasizing correct identification of features. The right whisker extends from Q3 (4 books) to the max (15 books), confirming choice A as consistent with the five-number summary. The box spans Q1 (1) to Q3 (4), with median at 2, and left whisker from min (0) to Q1. Distractors include choice D, confusing IQR (3 books) with range (15), and choice B, incorrectly extending the left whisker to the median. A mini-lesson on boxplots: they divide data into quartiles, with the box showing IQR for spread, median for location, and whiskers for overall range, useful for visualizing skewness, evident here by the extended right whisker indicating right-skewness.

Question 16

1. The box extends from 0 to 15 because those are the smallest and largest values.
2. The median line is at 2, and the box extends from 1 to 4. (correct answer)
3. The IQR is $15-0=15$, so the box length is 15.
4. The left whisker ends at 2 because whiskers end at the median.
5. The value 15 must be plotted as an outlier point and cannot be a whisker endpoint.

Explanation: This question in AP Statistics examines boxplots, which graphically depict the five-number summary to summarize data distribution. The box extends from Q1=1 to Q3=4, with the median at 2 inside, whiskers from 1 to min=0 on the left and 4 to max=15 on the right, as no outliers are marked. Choice B correctly identifies the median at 2 and box from 1 to 4, aligning with the statistics. Choice C is a distractor that wrongly equates the IQR with the range (15-0=15), but the IQR is 4-1=3, making the box length 3. Mini-lesson on boxplots: the box represents the IQR for the central 50%, the median line shows the midpoint, and whiskers extend to min and max, revealing skewness—such as the long right whisker suggesting right-skewed absences. This helps educators analyze attendance patterns visually.

Question 17

1. The box extends from 6 to 20 because it represents all fish lengths.
2. The median line is at 11, and the whiskers extend to 6 and 20. (correct answer)
3. The right whisker ends at 14 because whiskers cannot go beyond $Q_3$.
4. The IQR is $20-6=14$, so the box length is 14 inches.
5. The median is at 9 because the median is always $Q_1$ for a boxplot.

Explanation: The skill tested is understanding boxplots in AP Statistics, which use the five-number summary for data visualization. The box extends from Q1=9 to Q3=14, median at 11 inside, whiskers to min=6 and max=20. Choice B correctly notes the median at 11 and whiskers to 6 and 20, aligning with the statistics. A distractor like choice D incorrectly sets IQR as range (20-6=14), but true IQR is 14-9=5, box length 5 inches. To interpret boxplots: the box shows IQR (middle 50%), median divides it, whiskers reach min/max, revealing distribution shape—symmetric here but with possible outliers in fish lengths. This aids in ecological data analysis.

Question 18

1. The box extends from 245 to 310, and the median line is at 270. (correct answer)
2. The median line is at 245 because the median equals $Q_1$.
3. The IQR is $420-210=210$, so the box length is 210 ms.
4. The whiskers extend from 245 to 310, and the box extends from 210 to 420.
5. The maximum 420 must be displayed as an outlier point beyond the whisker.

Explanation: This AP Statistics question involves interpreting boxplots, which represent the five-number summary graphically. The box is from Q1=245 to Q3=310, with median at 270 inside, whiskers to min=210 and max=420. Choice A accurately states the box from 245 to 310 with median at 270, consistent with the summary. Choice C distracts by misstating the IQR as the range (420-210=210), but the actual IQR is 310-245=65, so box length is 65 ms. Mini-lesson on reading boxplots: the box encloses the IQR for central data, median line at 50th percentile, whiskers to extremes, highlighting potential skew—like the longer right whisker in reaction times. Such plots are valuable for comparing groups in research studies.

Question 19

1. The box should start at 92 and end at 131 because it contains all data values.
2. The median line should be drawn at 112, inside the box from 105 to 120. (correct answer)
3. The left whisker should end at 105 because whiskers always end at $Q_1$.
4. The IQR is $131-92=39$, so the box length is 39 cm.
5. Because the maximum is 131, the right whisker must be omitted and replaced with a dot.

Explanation: The skill here involves graphical representations of summary statistics in AP Statistics, particularly constructing and interpreting boxplots from the five-number summary. The box is drawn from Q1=105 to Q3=120, with the median line at 112 inside it, left whisker from 105 to min=92, and right whisker from 120 to max=131. Choice B accurately states the median at 112 within the box from 105 to 120, consistent with the data. A distractor such as choice D miscalculates the IQR as the range (131-92=39), but the true IQR is 120-105=15, so the box length is 15 cm. To read boxplots: note the box spans the middle 50% (IQR), the median divides it, and whiskers reach extremes, providing insights into variability and potential outliers in plant heights. This visual tool is essential for summarizing and comparing biological measurements efficiently.

Question 20

1. The median is at 12.5 and must be located at the right edge of the box.
2. The box extends from 10.0 to 15.0 with a median line at 12.5. (correct answer)
3. The whiskers extend from 10.0 to 15.0 because whiskers show the middle 50%.
4. The IQR is $22.0-8.5=13.5$, so the box length is 13.5.
5. The minimum 8.5 is plotted as an outlier point instead of a whisker endpoint.

Explanation: In AP Statistics, this question tests understanding of boxplots as visual summaries of the five-number summary. The box spans from Q1=10.0 to Q3=15.0, with the median line at 12.5 inside, whiskers to min=8.5 and max=22.0. Choice B correctly describes the box from 10.0 to 15.0 with median at 12.5, matching the data. A distractor like choice E assumes the min=8.5 is an outlier, but the boxplot uses whiskers to extremes without specifying outlier detection. For a mini-lesson: in boxplots, the box covers the IQR (15.0-10.0=5.0), representing middle 50%, while whiskers show full spread, aiding in identifying asymmetry in car prices. This graphical tool facilitates quick comparisons across dealerships or months.