Display Data in Statistical Plots - 6th Grade Math

1. A set of 9 test scores is: 70, 72, 75, 75, 78, 80, 84, 88, 90. Which option gives the correct five-number summary for a box plot?
   Answer: min 70, $Q_1$ 73.5, median 78, $Q_3$ 86, max 90 Tests displaying numerical data in statistical plots on number line: dot plots (dots stacked at values), histograms (bars for binned intervals), box plots (five-number summary with box and whiskers). Dot plot: number line with values, stack dots vertically above each value (if data has three 7's, three dots stacked at 7 on number line, shows frequency by stack height and distribution by position). Histogram: bin data into intervals (60-69, 70-79, etc.), draw bars with heights=frequencies (7 students scored 70-79: bar height 7), bars touch (continuous data), shows shape (symmetric, skewed) and frequency distribution. Box plot: five-number summary (min, Q1, median, Q3, max), draw box from Q1 to Q3 (IQR=middle 50%), line at median inside box, whiskers extend to min and max (shows spread and center, identifies outliers if beyond whiskers). For the sorted data 70,72,75,75,78,80,84,88,90, the correct five-number summary is min 70, Q1 73.5 (average of 72 and 75, middle of lower half), median 78, Q3 86 (average of 84 and 88, middle of upper half), max 90. Errors include wrong Q1 like 72 or incorrect min. Creating a box plot: sort data, compute summary excluding median from halves for quartiles, draw accordingly; this highlights the spread with IQR of 12.5.
2. Based on the histogram shown, which statement about the data distribution is most accurate?
   Answer: The data shows that most values fall between 10-20 with some higher values Looking at the histogram, the bars for intervals 10-15 and 15-20 are the tallest (heights of 8 and 6 respectively), indicating most data falls in the 10-20 range. The bars for 20-25 and 25-30 show some data at higher values but much less frequency. Choice A incorrectly identifies the peak range. Choice C misidentifies where most data occurs. Choice D is wrong since the bars have clearly different heights showing unequal distribution.
3. Marcus recorded the number of books read by students in his class over summer vacation: 3, 5, 2, 7, 3, 8, 4, 3, 6, 5, 2, 4, 3, 7, 5. He wants to create a dot plot to display this data. If he sets up his number line from 0 to 10, how many dots will be stacked above the value 3?
   Answer: 4 dots because 3 appears 4 times in the data set In a dot plot, each occurrence of a value gets represented by one dot stacked above that value on the number line. Counting the occurrences of 3 in the data: 3, 5, 2, 7, 3, 8, 4, 3, 6, 5, 2, 4, 3, 7, 5. The value 3 appears exactly 4 times, so 4 dots will be stacked above 3. Choice A miscounts by one. Choice C confuses the concept by counting nearby values. Choice D incorrectly uses the position of the first 3 in the list.
4. Based on the histogram shown, if this same data were displayed as a dot plot instead, how many total dots would appear above the number line?
   Answer: 12 dots total, representing the sum of all frequency values In a dot plot, each individual data point gets one dot, so the total number of dots equals the total number of data points collected. From the histogram, we add up all the frequencies: 3 + 5 + 2 + 2 = 12 total data points. Therefore, a dot plot of this same data would show 12 dots total distributed across the number line. Choice B confuses the number of intervals with data points. Choice C uses only the highest frequency. Choice D incorrectly doubles the calculation.
5. A student created a dot plot for the data set: 2, 4, 4, 6, 6, 6, 8, 8. If she wants to convert this into a histogram with bin width of 2 (intervals: 1-2, 3-4, 5-6, 7-8), which interval will have a frequency that differs most from what the dot plot shows for individual values?
   Answer: Interval 5-6 will differ most because it has the highest individual frequencies In the dot plot, individual values show: 2(1 dot), 4(2 dots), 6(3 dots), 8(2 dots). In the histogram: interval 1-2 has frequency 1, interval 3-4 has frequency 2, interval 5-6 has frequency 3, interval 7-8 has frequency 2. The 5-6 interval combines the most individual data points (3) and shows the biggest change from individual value representation to grouped representation. Choice A is wrong because 1-2 only has one value. Choice B has a moderate change. Choice D incorrectly focuses on numerical range rather than frequency differences.
6. The heights (in inches) of 8 plants are: 12, 13, 13, 14, 15, 16, 16, 20. Which option correctly describes the box plot that should be drawn on a number line?
   Answer: Min 12, $Q_1=13$, median 14.5, $Q_3=16$, max 20 (box from 13 to 16 with median at 14.5; whiskers to 12 and 20). Tests displaying numerical data in statistical plots on number line: dot plots (dots stacked at values), histograms (bars for binned intervals), box plots (five-number summary with box and whiskers). Dot plot: number line with values, stack dots vertically above each value (if data has three 7's, three dots stacked at 7 on number line, shows frequency by stack height and distribution by position). Histogram: bin data into intervals (60-69, 70-79, etc.), draw bars with heights=frequencies (7 students scored 70-79: bar height 7), bars touch (continuous data), shows shape (symmetric, skewed) and frequency distribution. Box plot: five-number summary (min, Q1, median, Q3, max), draw box from Q1 to Q3 (IQR=middle 50%), line at median inside box, whiskers extend to min and max (shows spread and center, identifies outliers if beyond whiskers). For example, box plot: data 20,25,30,35,40,50,60 gives min=20, Q1=27.5, median=35, Q3=45, max=60, plot shows box from 27.5 to 45, line at 35, whiskers to 20 and 60. The correct box plot uses min 12, Q1=13, median 14.5, Q3=16, max 20, which is option A. An error would be box from min to max as in D, or incorrect median like 15 in C. Box plot: (1) find five-number summary (min, Q1, median, Q3, max from ordered data), (2) draw box from Q1 to Q3, (3) line at median, (4) whiskers to min/max. Interpreting: box plot shows spread (IQR, range) and center (median). Mistakes: wrong median calculation for even n (average of 4th and 5th), incorrect Q1/Q3, or scale issues.
7. A teacher has 30 test scores and wants to show the overall shape of the distribution without listing every exact score. Which plot type is the best choice?
   Answer: Histogram Tests displaying numerical data in statistical plots on number line: dot plots (dots stacked at values), histograms (bars for binned intervals), box plots (five-number summary with box and whiskers). Dot plot: number line with values, stack dots vertically above each value (if data has three 7's, three dots stacked at 7 on number line, shows frequency by stack height and distribution by position). Histogram: bin data into intervals (60-69, 70-79, etc.), draw bars with heights=frequencies (7 students scored 70-79: bar height 7), bars touch (continuous data), shows shape (symmetric, skewed) and frequency distribution. Box plot: five-number summary (min, Q1, median, Q3, max), draw box from Q1 to Q3 (IQR=middle 50%), line at median inside box, whiskers extend to min and max (shows spread and center, identifies outliers if beyond whiskers). For example, histogram: scores binned 60-69(3), 70-79(7), 80-89(5), 90-100(2), bars touching at heights 3,7,5,2. The best plot type to show overall shape for 30 scores without exact values is histogram, which is option B. An error would be dot plot which shows exact values but may be cluttered for 30 data points, or picture graph not suitable for numerical distribution. Histogram: (1) bin data (group into intervals: 0-9, 10-19, etc.), (2) count frequency per bin, (3) draw bars touching with heights=frequencies. Interpreting: histogram shows shape and frequency distribution. Mistakes: choosing plot type inappropriate for data size, like dot plot for large sets or tally chart without visual distribution.
8. A teacher recorded the number of books 10 students read over the summer: 1, 2, 2, 3, 3, 3, 4, 5, 5, 6. Which option shows the correct dot plot on a number line from 1 to 6 (one dot per student, stacked above each value)?
   Answer: Dot plot counts: 1→1 dot, 2→2 dots, 3→3 dots, 4→1 dot, 5→2 dots, 6→1 dot (stacked vertically above each number 1–6). Tests displaying numerical data in statistical plots on number line: dot plots (dots stacked at values), histograms (bars for binned intervals), box plots (five-number summary with box and whiskers). Dot plot: number line with values, stack dots vertically above each value (if data has three 7's, three dots stacked at 7 on number line, shows frequency by stack height and distribution by position). Histogram: bin data into intervals (60-69, 70-79, etc.), draw bars with heights=frequencies (7 students scored 70-79: bar height 7), bars touch (continuous data), shows shape (symmetric, skewed) and frequency distribution. Box plot: five-number summary (min, Q1, median, Q3, max), draw box from Q1 to Q3 (IQR=middle 50%), line at median inside box, whiskers extend to min and max (shows spread and center, identifies outliers if beyond whiskers). For the data 1,2,2,3,3,3,4,5,5,6, the correct dot plot has counts 1→1 dot, 2→2 dots, 3→3 dots, 4→1 dot, 5→2 dots, 6→1 dot, stacked vertically. Errors include incorrect counts like swapping frequencies or placing dots horizontally instead of stacking. Creating a dot plot involves drawing a number line from min to max, placing a dot for each data point above its value, and stacking for repeats; this plot shows the mode at 3 with the tallest stack.
9. A student recorded 12 daily temperatures (in $^\circ$F): 62, 62, 63, 64, 64, 64, 65, 66, 66, 67, 68, 68. Which type of plot would be the best choice to show the exact values and how often each temperature occurred?
   Answer: Dot plot Tests displaying numerical data in statistical plots on number line: dot plots (dots stacked at values), histograms (bars for binned intervals), box plots (five-number summary with box and whiskers). Dot plot: number line with values, stack dots vertically above each value (if data has three 7's, three dots stacked at 7 on number line, shows frequency by stack height and distribution by position). Histogram: bin data into intervals (60-69, 70-79, etc.), draw bars with heights=frequencies (7 students scored 70-79: bar height 7), bars touch (continuous data), shows shape (symmetric, skewed) and frequency distribution. Box plot: five-number summary (min, Q1, median, Q3, max), draw box from Q1 to Q3 (IQR=middle 50%), line at median inside box, whiskers extend to min and max (shows spread and center, identifies outliers if beyond whiskers). For showing exact temperatures like 62 (twice), 64 (thrice) and their frequencies in a small dataset, the best choice is a dot plot, which displays each value with stacked dots for repeats. Other plots like histograms bin values losing exactness, box plots summarize without frequencies, and pie charts suit categorical data not numerical. Choosing and creating: select dot plot for precise value display; mistakes include using histograms for small exact data sets.
10. A student collected 12 quiz scores (out of 10): 6, 7, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10. Which display is the best choice to show the exact scores and how often each score occurs?
    Answer: Dot plot (shows each exact score and stacks to show frequency). Tests displaying numerical data in statistical plots on number line: dot plots (dots stacked at values), histograms (bars for binned intervals), box plots (five-number summary with box and whiskers). Dot plot: number line with values, stack dots vertically above each value (if data has three 7's, three dots stacked at 7 on number line, shows frequency by stack height and distribution by position); Histogram: bin data into intervals (60-69, 70-79, etc.), draw bars with heights=frequencies (7 students scored 70-79: bar height 7), bars touch (continuous data), shows shape (symmetric, skewed) and frequency distribution; Box plot: five-number summary (min, Q1, median, Q3, max), draw box from Q1 to Q3 (IQR=middle 50%), line at median inside box, whiskers extend to min and max (shows spread and center, identifies outliers if beyond whiskers). For example, data 5,6,6,7,7,7,8,8,10 displayed as dot plot: number line 5-10, stack dots (one at 5, two at 6, three at 7, two at 8, one at 10, shows mode at 7 with most dots); or histogram: scores binned 60-69(3), 70-79(7), 80-89(5), 90-100(2), bars touching at heights 3,7,5,2; or box plot: data 20,25,30,35,40,50,60 gives min=20, Q1=27.5, median=35, Q3=45, max=60, plot shows box from 27.5 to 45, line at 35, whiskers to 20 and 60. The best choice for showing exact quiz scores and frequencies is choice A, a dot plot that displays each value with stacked dots for counts. Common errors include choosing a histogram that bins data and hides exact values (choice B), a box plot that only shows summaries (choice C), or a line graph unsuitable for distributions (choice D). Creating dot plot: (1) draw number line with appropriate scale (min to max of data), (2) mark each data value with dot above number line, (3) stack dots if repeated values (three 7's→three dots stacked at 7). Interpreting: dot plot shows exact values and mode (most dots), histogram shows shape and frequency distribution, box plot shows spread (IQR, range) and center (median); Mistakes: dot plot stacking horizontal, histogram gaps, box plot box wrong extent, scale issues, frequency errors.
11. A cafeteria tracked the number of apples sold each day for 10 days: 18, 18, 19, 20, 20, 20, 21, 22, 22, 24. Which dot plot is correct on a number line from 18 to 24?
    Answer: Dots at 18(2), 19(1), 20(3), 21(1), 22(2), 23(0), 24(1), stacked vertically above 18–24. A dot plot shows how often each number appears by stacking one dot for each time it shows up. Your job is to count and stack! Start by tallying each value in the list: $18, 18, 19, 20, 20, 20, 21, 22, 22, 24$. - $18$ appears $2$ times → $2$ dots - $19$ appears $1$ time → $1$ dot - $20$ appears $3$ times → $3$ dots - $21$ appears $1$ time → $1$ dot - $22$ appears $2$ times → $2$ dots - $23$ appears $0$ times → no dots - $24$ appears $1$ time → $1$ dot Notice $23$ still gets its own spot on the number line, even with zero dots, so the spacing stays even. Think of it like stacking blocks above each number's house. No visitors? The house is still there, just empty! Try this at home: tally how many socks you own of each color and build your own dot plot!
12. A science class measured plant heights (in cm) for 9 plants: 8, 9, 9, 10, 10, 10, 11, 12, 12. Which option correctly describes the dot plot on a number line from 8 to 12?
    Answer: Counts: 8→1, 9→2, 10→3, 11→1, 12→2 (stacked vertically above 8–12). Tests displaying numerical data in statistical plots on number line: dot plots (dots stacked at values), histograms (bars for binned intervals), box plots (five-number summary with box and whiskers). Dot plot: number line with values, stack dots vertically above each value (if data has three 7's, three dots stacked at 7 on number line, shows frequency by stack height and distribution by position). Histogram: bin data into intervals (60-69, 70-79, etc.), draw bars with heights=frequencies (7 students scored 70-79: bar height 7), bars touch (continuous data), shows shape (symmetric, skewed) and frequency distribution. Box plot: five-number summary (min, Q1, median, Q3, max), draw box from Q1 to Q3 (IQR=middle 50%), line at median inside box, whiskers extend to min and max (shows spread and center, identifies outliers if beyond whiskers). For the data 8,9,9,10,10,10,11,12,12, the correct dot plot has counts 8→1, 9→2, 10→3, 11→1, 12→2, stacked vertically on an even scale from 8 to 12. Errors include incorrect counts like 10→2 instead of 3 or using an uneven scale that skips values. Creating a dot plot: draw number line from min to max, place dots above values and stack repeats; this reveals the mode at 10 with the highest stack.
13. A teacher recorded how many books 10 students read over the summer: 1, 2, 2, 3, 3, 3, 4, 4, 5, 5. Which dot plot correctly displays the data on a number line from 1 to 5 (stack dots vertically above each value)?
    Answer: Dots at 1(1), 2(2), 3(3), 4(2), 5(2), stacked vertically above 1–5 on an even scale. Tests displaying numerical data in statistical plots on number line: dot plots (dots stacked at values), histograms (bars for binned intervals), box plots (five-number summary with box and whiskers). Dot plot: number line with values, stack dots vertically above each value (if data has three 7's, three dots stacked at 7 on number line, shows frequency by stack height and distribution by position); Histogram: bin data into intervals (60-69, 70-79, etc.), draw bars with heights=frequencies (7 students scored 70-79: bar height 7), bars touch (continuous data), shows shape (symmetric, skewed) and frequency distribution; Box plot: five-number summary (min, Q1, median, Q3, max), draw box from Q1 to Q3 (IQR=middle 50%), line at median inside box, whiskers extend to min and max (shows spread and center, identifies outliers if beyond whiskers). For example, data 5,6,6,7,7,7,8,8,10 displayed as dot plot: number line 5-10, stack dots (one at 5, two at 6, three at 7, two at 8, one at 10, shows mode at 7 with most dots); or histogram: scores binned 60-69(3), 70-79(7), 80-89(5), 90-100(2), bars touching at heights 3,7,5,2; or box plot: data 20,25,30,35,40,50,60 gives min=20, Q1=27.5, median=35, Q3=45, max=60, plot shows box from 27.5 to 45, line at 35, whiskers to 20 and 60. The correct dot plot for the books read data is choice A, with dots stacked vertically at 1(1), 2(2), 3(3), 4(2), 5(2) on an even scale from 1 to 5, accurately showing the frequencies. Common errors include spreading dots horizontally instead of stacking (choice B), incorrect frequency counts like swapping 2 and 3 (choice C), or using an uneven scale that distorts the data (choice D). Creating dot plot: (1) draw number line with appropriate scale (min to max of data), (2) mark each data value with dot above number line, (3) stack dots if repeated values (three 7's→three dots stacked at 7). Interpreting: dot plot shows exact values and mode (most dots), histogram shows shape and frequency distribution, box plot shows spread (IQR, range) and center (median); Mistakes: dot plot stacking horizontal, histogram gaps, box plot box wrong extent, scale issues, frequency errors.
14. A researcher has collected data and wants to choose between displaying it as a histogram or a dot plot. Her data set contains the values: 12, 12, 12, 12, 14, 14, 16, 18, 18, 20. Which statement best describes how the choice of display method would affect the interpretation of this data?
    Answer: A dot plot would better show the exact frequency of repeated values like 12 A dot plot would stack 4 dots above the value 12, clearly showing that 12 appears exactly 4 times in the dataset. It would also stack 2 dots above 14 and 2 above 18, making the frequencies of repeated values immediately visible. A histogram with intervals would group values together (like 12-15 containing both 12s and 14s), making it harder to see the exact frequency of individual values. Choice A reverses this relationship. Choice C is incorrect because the displays show information differently. Choice D is wrong because dot plots actually show individual values clearly, including potential outliers.
15. A class collected 14 temperatures (in °F) from a week of mornings and afternoons: 61, 62, 62, 63, 64, 64, 65, 65, 66, 66, 67, 68, 68, 70. Which plot type is best for showing the overall shape of the distribution without needing to see every exact value?
    Answer: Histogram (groups data into intervals to show the shape clearly). Tests displaying numerical data in statistical plots on number line: dot plots (dots stacked at values), histograms (bars for binned intervals), box plots (five-number summary with box and whiskers). Dot plot: number line with values, stack dots vertically above each value (if data has three 7's, three dots stacked at 7 on number line, shows frequency by stack height and distribution by position); Histogram: bin data into intervals (60-69, 70-79, etc.), draw bars with heights=frequencies (7 students scored 70-79: bar height 7), bars touch (continuous data), shows shape (symmetric, skewed) and frequency distribution; Box plot: five-number summary (min, Q1, median, Q3, max), draw box from Q1 to Q3 (IQR=middle 50%), line at median inside box, whiskers extend to min and max (shows spread and center, identifies outliers if beyond whiskers). For example, data 5,6,6,7,7,7,8,8,10 displayed as dot plot: number line 5-10, stack dots (one at 5, two at 6, three at 7, two at 8, one at 10, shows mode at 7 with most dots); or histogram: scores binned 60-69(3), 70-79(7), 80-89(5), 90-100(2), bars touching at heights 3,7,5,2; or box plot: data 20,25,30,35,40,50,60 gives min=20, Q1=27.5, median=35, Q3=45, max=60, plot shows box from 27.5 to 45, line at 35, whiskers to 20 and 60. The best plot for showing the overall shape of temperatures without exact values is choice A, a histogram that groups data into intervals. Common errors include selecting a dot plot that emphasizes exact values (choice B), a non-standard picture graph (choice C), or a stem-and-leaf plot not among the typical choices (choice D). Creating dot plot: (1) draw number line with appropriate scale (min to max of data), (2) mark each data value with dot above number line, (3) stack dots if repeated values (three 7's→three dots stacked at 7); Histogram: (1) bin data (group into intervals: 0-9, 10-19, etc.), (2) count frequency per bin, (3) draw bars touching with heights=frequencies. Box plot: (1) find five-number summary (min, Q1, median, Q3, max from ordered data), (2) draw box from Q1 to Q3, (3) line at median, (4) whiskers to min/max; Interpreting: dot plot shows exact values and mode (most dots), histogram shows shape and frequency distribution, box plot shows spread (IQR, range) and center (median); Mistakes: dot plot stacking horizontal, histogram gaps, box plot box wrong extent, scale issues, frequency errors.
16. Sarah collected data on the heights (in inches) of players on her basketball team: 58, 60, 62, 64, 66, 68, 70. She wants to create a box plot for this data. What will be the position of the median line in her box plot?
    Answer: At 64 inches, which is the middle value of the seven data points For an odd number of data points (7 in this case), the median is the middle value when the data is arranged in order. Since there are 7 values, the median is the 4th value: 58, 60, 62, 64, 66, 68, 70. So the median line in the box plot will be at 64 inches. Choice B confuses position with value. Choice C incorrectly applies the even-number median rule. Choice D confuses median with mean.
17. A gym tracked how many minutes 14 students exercised in one day and grouped the data: - 0–9 minutes: 1 student - 10–19 minutes: 4 students - 20–29 minutes: 6 students - 30–39 minutes: 3 students Which histogram description is correct?
    Answer: Bars for 0–9, 10–19, 20–29, 30–39 have heights 1, 4, 6, 3, and the bars touch. Tests displaying numerical data in statistical plots on number line: dot plots (dots stacked at values), histograms (bars for binned intervals), box plots (five-number summary with box and whiskers). Dot plot: number line with values, stack dots vertically above each value (if data has three 7's, three dots stacked at 7 on number line, shows frequency by stack height and distribution by position). Histogram: bin data into intervals (60-69, 70-79, etc.), draw bars with heights=frequencies (7 students scored 70-79: bar height 7), bars touch (continuous data), shows shape (symmetric, skewed) and frequency distribution. Box plot: five-number summary (min, Q1, median, Q3, max), draw box from Q1 to Q3 (IQR=middle 50%), line at median inside box, whiskers extend to min and max (shows spread and center, identifies outliers if beyond whiskers). The correct histogram has bars for 0–9 (height 1), 10–19 (4), 20–29 (6), 30–39 (3), with bars touching. Errors include gaps, incorrect heights like swapping 4 and 6, or wrong counts. Creating a histogram: bin the data, count per bin, draw touching bars; interpreting reveals most students exercised 20–29 minutes.
18. A science class measured plant heights (in cm): 12, 14, 15, 15, 16, 18, 20, 21. A student wants to show the five-number summary on a number line using a box plot. Which option describes the correct box plot?
    Answer: Min 12, $Q_1=14.5$, median 15.5, $Q_3=19$, max 21; box from 14.5 to 19 with a median line at 15.5; whiskers to 12 and 21. Tests displaying numerical data in statistical plots on number line: dot plots (dots stacked at values), histograms (bars for binned intervals), box plots (five-number summary with box and whiskers). Dot plot: number line with values, stack dots vertically above each value (if data has three 7's, three dots stacked at 7 on number line, shows frequency by stack height and distribution by position); Histogram: bin data into intervals (60-69, 70-79, etc.), draw bars with heights=frequencies (7 students scored 70-79: bar height 7), bars touch (continuous data), shows shape (symmetric, skewed) and frequency distribution; Box plot: five-number summary (min, Q1, median, Q3, max), draw box from Q1 to Q3 (IQR=middle 50%), line at median inside box, whiskers extend to min and max (shows spread and center, identifies outliers if beyond whiskers). For example, data 5,6,6,7,7,7,8,8,10 displayed as dot plot: number line 5-10, stack dots (one at 5, two at 6, three at 7, two at 8, one at 10, shows mode at 7 with most dots); or histogram: scores binned 60-69(3), 70-79(7), 80-89(5), 90-100(2), bars touching at heights 3,7,5,2; or box plot: data 20,25,30,35,40,50,60 gives min=20, Q1=27.5, median=35, Q3=45, max=60, plot shows box from 27.5 to 45, line at 35, whiskers to 20 and 60. The correct box plot for the plant heights is choice A, with min 12, Q1=14.5, median 15.5, Q3=19, max 21, box from 14.5 to 19, median line at 15.5, and whiskers to 12 and 21. Common errors include incorrect quartiles and boxing from min to max (choice B), missing the median line (choice C), or wrong five-number summary values (choice D). Creating dot plot: (1) draw number line with appropriate scale (min to max of data), (2) mark each data value with dot above number line, (3) stack dots if repeated values (three 7's→three dots stacked at 7); Box plot: (1) find five-number summary (min, Q1, median, Q3, max from ordered data), (2) draw box from Q1 to Q3, (3) line at median, (4) whiskers to min/max. Interpreting: dot plot shows exact values and mode (most dots), histogram shows shape and frequency distribution, box plot shows spread (IQR, range) and center (median); Mistakes: dot plot stacking horizontal, histogram gaps, box plot box wrong extent, scale issues, frequency errors.
19. Looking at the box plot, what can you conclude about the distribution of the data compared to what a dot plot of the same data would reveal?
    Answer: The box plot shows quartile positions, while a dot plot would show individual data points Box plots display the five-number summary (minimum, Q1, median, Q3, maximum) and show the quartile positions and spread, but they don't show individual data points or their frequencies. Dot plots show every individual data point as a dot, revealing the exact frequency of each value and the shape of the distribution. Choice A reverses the characteristics. Choice C is incorrect because box plots show medians, not means. Choice D is wrong because both plots can show extreme values, though differently.
20. Looking at the dot plot, if you were to convert this data into a histogram with intervals 0-2, 3-5, 6-8, and 9-11, which interval would have the highest frequency bar?
    Answer: The 3-5 interval would be highest with 6 data points total From the dot plot, counting dots in each interval: 0-2 interval (values 0,1,2) has 2+1+1=4 dots total. 3-5 interval (values 3,4,5) has 2+3+1=6 dots total. 6-8 interval (values 6,7,8) has 1+2+0=3 dots total. 9-11 interval (values 9,10) has 1+1=2 dots total. The 3-5 interval has the most data points (6), so it would have the highest bar in a histogram. Choices A, C, and D either miscount the dots or incorrectly identify which interval has the most data.

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