Display Data in Statistical Plots
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6th Grade Math › Display Data in Statistical Plots
A set of 7 ages (in years) is: 11, 12, 12, 13, 14, 15, 16. Which box plot description is correct?
(Use the five-number summary: min, $Q_1$, median, $Q_3$, max.)
Five-number summary: min 11, $Q_1$ 12, median 13, $Q_3$ 15, max 16. Box from 12 to 15 with a median line at 13; whiskers to 11 and 16.
Five-number summary: min 11, $Q_1$ 12, median 13, $Q_3$ 14, max 16. Box from 12 to 14 with a median line at 13; whiskers to 11 and 16.
Box goes from min 11 to max 16, with whiskers drawn from 12 to 15 and a median line at 13.
Five-number summary: min 11, $Q_1$ 12, median 13, $Q_3$ 15, max 16, but the median line is missing inside the box.
Explanation
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 11,12,12,13,14,15,16, the correct box plot uses min 11, Q1 12 (median of lower half 11,12,12), median 13, Q3 15 (median of upper half 14,15,16), max 16, with box from 12 to 15, median line at 13, and whiskers to 11 and 16. Errors include wrong Q3 like 14 or boxing from min to max. Creating a box plot: order data, find five-number summary, draw box and whiskers; this shows the data is fairly symmetric around the median.
A teacher summarizes the number of minutes students spent reading last night using these bins:
0–9: 1 student
10–19: 4 students
20–29: 6 students
30–39: 3 students
Which histogram is correct?
Bars for 0–9, 10–19, 20–29, 30–39 with heights 2, 4, 6, 3, and the bars touch.
Bars for 0–9, 10–19, 20–29, 30–39 with heights 1, 4, 6, 3, and the bars touch.
Bars for 0–9, 10–19, 20–29, 30–39 with heights 1, 4, 6, 3, but the bars are separated by gaps.
Bars for 0–9, 10–19, 20–29, 30–39 with heights 1, 6, 4, 3, and the bars touch.
Explanation
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 histogram for reading minutes is choice A, with bars touching and heights 1, 4, 6, 3 for bins 0–9, 10–19, 20–29, 30–39. Common errors include separating bars with gaps (choice B), swapping heights like 4 and 6 (choice C), or incorrect frequencies such as starting with 2 (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.
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?
Min 12, $Q_1=14$, median 15.5, $Q_3=20$, max 21; box from 12 to 21 with a median line at 15.5.
Min 12, $Q_1=14.5$, median 15.5, $Q_3=19$, max 21; box from 14.5 to 19 but no median line is shown.
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.
Min 12, $Q_1=15$, median 16, $Q_3=20$, max 21; box from 15 to 20 with whiskers to 12 and 21.
Explanation
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.
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)?
Dot plot counts: 1→1 dot, 2→3 dots, 3→2 dots, 4→1 dot, 5→2 dots, 6→1 dot (stacked vertically above each number 1–6).
Dot plot counts: 1→1 dot, 2→2 dots, 3→3 dots, 4→1 dot, 5→1 dot, 6→1 dot (stacked vertically above each number 1–6).
Dots are placed in a row (not stacked): one dot above 1, two dots spread horizontally above 2, three dots spread horizontally above 3, one above 4, two above 5, one above 6.
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).
Explanation
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.
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?
Dot plot
Circle (pie) chart
Box plot
Histogram
Explanation
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.
A student recorded the number of pages read each day for 10 days: 8, 10, 10, 12, 12, 12, 13, 15, 15, 18. The student wants a plot that shows each exact value and how often it occurs. Which plot type is the best choice?
Line graph
Box plot
Dot plot
Histogram
Explanation
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). The best plot type to show each exact value and frequency is dot plot, which is option B. An error would be choosing histogram which bins data and hides exact values, or box plot which summarizes without frequencies. 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). Mistakes: choosing inappropriate plot type for small data sets where exact values are needed.
A student recorded the ages (in years) of 10 kids at a sports camp: 10, 10, 11, 11, 11, 12, 12, 13, 14, 14. Which dot plot correctly represents the data on a number line from 10 to 14?
Dots at 10(2), 11(3), 12(2), 13(1), 14(2), stacked vertically above 10–14 on an even scale.
Dots at 10(2), 11(3), 12(2), 13(1), 14(2), but the dots are placed below the number line and do not line up with the values.
Dots at 10(2), 11(2), 12(3), 13(1), 14(2), stacked vertically above 10–14.
Dots at 10(1), 11(3), 12(2), 13(1), 14(3), stacked vertically above 10–14.
Explanation
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 kids' ages is choice A, with dots stacked vertically at 10(2), 11(3), 12(2), 13(1), 14(2) on an even scale from 10 to 14. Common errors include swapping frequencies like 11(2) and 12(3) (choice B), misplacing dots below the line (choice C), or incorrect counts such as 10(1) and 14(3) (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.
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?
Dots at 18(2), 19(1), 20(3), 21(1), 22(2), 23(0), 24(1), stacked vertically above 18–24.
Dots at 18(1), 19(1), 20(3), 21(1), 22(2), 23(0), 24(2), stacked vertically above 18–24.
Dots at 18(2), 19(1), 20(3), 21(1), 22(2), 23(1), 24(0), stacked vertically above 18–24.
Dots at 18(2), 19(1), 20(3), 21(1), 22(2), 24(1) but the scale skips 23 and jumps from 22 to 24.
Explanation
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 apples sold is choice A, with dots at 18(2), 19(1), 20(3), 21(1), 22(2), 23(0), 24(1) stacked vertically from 18 to 24. Common errors include wrong frequencies like 18(1) and 24(2) (choice B), skipping values on the scale like 23 (choice C), or incorrect counts such as 23(1) and 24(0) (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.
A teacher grouped quiz scores into intervals. The counts are: 60–69: 2 students, 70–79: 5 students, 80–89: 4 students, 90–99: 1 student. Which option describes the correct histogram (bars touch, x-axis shows the score intervals, y-axis shows frequency)?
Bars (touching) over 60–69, 70–79, 80–89, 90–99 with heights 2, 4, 5, 1.
Bars over 60–69, 70–79, 80–89, 90–99 with heights 2, 5, 4, 1, but there are gaps between the bars.
A bar chart with four separate categories labeled 60, 70, 80, 90 (not intervals), with heights 2, 5, 4, 1.
Bars (touching) over 60–69, 70–79, 80–89, 90–99 with heights 2, 5, 4, 1.
Explanation
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 correct histogram has touching bars with heights 2,5,4,1 over 60–69, 70–79, 80–89, 90–99, which is option A. An error would be bars with gaps as in option C, or using categories instead of intervals as in D. Histogram: (1) bin data (group into intervals: 60-69, etc.), (2) count frequency per bin, (3) draw bars touching with heights=frequencies. Interpreting: histogram shows shape and frequency distribution. Mistakes: gaps between bars, wrong heights like 4 instead of 5 for 70-79, or non-interval labels.
A cafeteria tracked how many apples were taken each day for 12 days: 18, 18, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23. Which option shows the correct dot plot on a number line from 18 to 23?
Dot counts: 18→1, 19→1, 20→3, 21→2, 22→3, 23→2 (stacked vertically above 18–23).
Dot counts: 18→2, 19→1, 20→3, 21→2, 22→3, 23→1, but the number line only goes from 18 to 22.
Dot counts: 18→2, 19→1, 20→3, 21→2, 22→3, 23→1 (stacked vertically above 18–23).
Dot counts: 18→2, 19→1, 20→2, 21→2, 22→3, 23→1 (stacked vertically above 18–23).
Explanation
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). The correct dot plot has dot counts 18→2, 19→1, 20→3, 21→2, 22→3, 23→1 stacked vertically, which is option A. An error would be incomplete scale missing 23 as in D, or wrong counts like 20→2 instead of 3 in B. 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 22's→three dots stacked at 22). Interpreting: dot plot shows exact values and mode (most dots, here at 20 and 22). Mistakes: frequency count wrong, scale doesn't include all data, or not stacking vertically.