Statistics Quiz: Representing Data With Number Line Plots

What this quiz covers

This quiz focuses on Representing Data With Number Line Plots, giving you a quick way to practice the rules, question types, and explanations that matter most for 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. Histogram counts: 0–4: 8, 5–9: 6, 10–14: 4.
2. Histogram counts: 0–4: 9, 5–9: 6, 10–14: 3.
3. Histogram counts: 0–4: 7, 5–9: 8, 10–14: 3.
4. Histogram counts: 0–4: 8, 5–9: 7, 10–14: 3. (correct answer)

Explanation: The plot is a histogram of wait times with bin width 5. Data values are counted into bins 0–4, 5–9, 10–14. Key features include high frequency in 0–4 with 8, decreasing to 3 in 10–14, spread from 1 to 14, right-skewed shape. The correct answer A matches because the counts are exactly 8,7,3 for the bins. A common misconception is to include boundary values in the wrong bin, like putting 5 in 0–4 instead of 5–9. To analyze, first check the scale and bin definitions. Then, count the points in each bin to confirm the heights.

Question 2

1. The distribution is strongly right-skewed because there are many low scores and only a few high scores.
2. The distribution is approximately symmetric because the scores increase gradually from 8 to 19 with similar counts in the middle. (correct answer)
3. The distribution is strongly left-skewed because there are many high scores and only a few low scores.
4. The distribution has a gap between 13 and 14 because no scores occur in that interval.

Explanation: The plot is a histogram of quiz scores. Data values are grouped into bins, with bar heights showing frequency in each bin. Key features include even distribution from 8 to 19, with clusters in the middle scores, spread of 11 points, and approximately symmetric shape. The correct answer B matches because the scores are balanced with gradual increase and similar counts around the center. A common misconception is to identify skew when the distribution is actually symmetric due to focusing on end bins only. To analyze, first check the scale and bin widths for proper grouping. Then, count data points in each bin to assess the shape and symmetry.

Question 3

1. The distribution is symmetric because the values are evenly balanced around 21 with equal tails.
2. The distribution is left-skewed because most values are around 24–28 with a few smaller values near 14–16.
3. The distribution is right-skewed because most values are around 18–23 with a few larger values near 26–28. (correct answer)
4. The distribution has a gap from 20 to 22 because no values occur in that interval.

Explanation: The plot is a dot plot of push-up counts. Each count is mapped as a dot on the number line, stacked for repeats. Key features include cluster around 20 with 3 dots, spread from 14 to 28, and right-skewed shape with longer tail to the right. The correct answer A matches because most values are in 18–23, with few larger ones extending to 28. A common misconception is to identify the skew based on the wrong direction of the tail. To analyze, first check the scale to see the range of push-ups. Then, count the dots to determine clusters and skew.

Question 4

1. The median is 67°F, and the range is 12°F.
2. The median is 68°F, and the range is 10°F.
3. The median is 67.5°F, and the range is 12°F. (correct answer)
4. The median is 68.5°F, and the range is 10°F.

Explanation: The plot is a box plot, summarizing the temperature data. The data values map to the plot by calculating quartiles, median, and extremes for the box and whiskers. Key features include the median at 67.5°F, box from Q1 to Q3 showing middle 50%, and whiskers to min 62°F and max 74°F, with no outliers. The correct answer A matches because the median is the average of 7th and 8th values (67+68)/2=67.5, and range is 74-62=12. A common misconception is to take the median as one of the middle values instead of averaging for even number of data points. To analyze, first check the scale to see the range of temperatures. Then, count the data points and sort them to verify the median and range.

Question 5

1. Dots at: 1.25(1), 1.50(2), 1.75(1), 2.00(2), 2.25(1), 2.50(2), 2.75(1), 3.00(1), 3.25(1). (correct answer)
2. Dots at: 1.25(1), 1.50(1), 1.75(1), 2.00(2), 2.25(1), 2.50(2), 2.75(1), 3.00(1), 3.25(2).
3. Dots at: 1.25(1), 1.50(2), 1.75(1), 2.00(2), 2.25(1), 2.50(1), 2.75(1), 3.00(1), 3.25(1).
4. Dots at: 1.25(1), 1.50(2), 1.75(1), 2.00(1), 2.25(1), 2.50(2), 2.75(2), 3.00(1), 3.25(1).

Explanation: The plot is a dot plot, displaying prices on a number line. Each price is mapped by placing a dot above its value, stacking for duplicates. Key features include clusters at 1.50, 2.00, 2.50 with 2 dots each, spread from 1.25 to 3.25, and a fairly uniform shape with increasing prices. The correct answer A matches because it accurately lists the positions and counts of dots for each price in the data. A common misconception is to forget to stack dots for repeated values, leading to incorrect counts. To analyze, first check the scale on the number line for the price range. Then, count the dots at each price to match the frequency in the data set.

Question 6

1. Dots at 14(1), 15(1), 16(3), 17(2), 18(2), 19(1), 21(1).
2. Dots at 14(1), 15(2), 16(2), 17(1), 18(2), 19(2), 21(1).
3. Dots at 14(2), 15(2), 16(3), 17(1), 18(1), 19(1), 21(1).
4. Dots at 14(1), 15(2), 16(3), 17(1), 18(2), 19(1), 21(1). (correct answer)

Explanation: A dot plot shows push-up counts as dots on a number line, with stacks like three at 16 and two at 15, 18. The data maps to dots at 14 (one), 15 (two), 16 (three), 17 (one), 18 (two), 19 (one), 21 (one), creating a cluster around 16 with tails. The plot features a peak at 16 and slight right skew to 21, spanning 14 to 21. Choice A correctly lists these frequencies for the visual representation. A common misconception is overlooking stacked dots as single points, but stacks indicate multiples. Check the number line scale from 14 to 21. Then, count dots per value to match the 11 students.

Question 7

1. The histogram would show a cluster in the 6–7 bin and a smaller right tail toward 10–11. (correct answer)
2. The histogram would be uniform because each bin has the same number of values.
3. The histogram would show a gap because there are no values in the 6–7 bin.
4. The histogram would be strongly left-skewed with most values in the 10–11 bin.

Explanation: A histogram groups waiting times into 2-minute bins on a number line, with bar heights showing counts like one in 2–3, five in 4–5, five in 6–7, three in 8–9, and two in 10–11. Data values fall into bins, creating a visual of higher bars in the middle and tapering off, especially to the right. Key features include a cluster around 6–7 minutes with a right tail extending to 10–11, indicating slight right skew and spread from 3 to 11. Choice A correctly describes this cluster and tail, aligning with the bin frequencies. A common misconception is thinking empty bins mean gaps in data, but here all bins have values except possibly unused ones outside the range. First, check the bin scale to ensure intervals like 2–3 capture values correctly. Then, count entries per bin to match the total of 16 times.

Question 8

1. The distribution is right-skewed because the upper end extends farther (up to 22) than the lower end. (correct answer)
2. The data are perfectly symmetric because the maximum and minimum are equally far from the median.
3. There is a gap between 18 and 19 inches that would appear as an empty space in a box plot.
4. The distribution is left-skewed because most values are close to 22 inches.

Explanation: A box plot summarizes data on a number line using a box for the middle 50% and whiskers for the extremes. The plant heights map to min at 14, Q1 at 15, median at 16.5, Q3 at 18, and max at 22, with the box from 15 to 18 and whiskers extending outward. Key features include a compact lower half and a longer upper whisker, showing right-skewed shape with spread from 14 to 22 and a potential outlier feel at 22. Choice B correctly identifies the right skew due to the upper end extending farther to 22. A common misconception is confusing skew with symmetry based only on min-max distance, but skew is about tail length and data density. Always check the number line scale to locate quartiles precisely. Then, count data points in each section to verify the five-number summary.

Question 9

1. Bars: 5–9 has 3 values; 10–14 has 8 values; 15–19 has 4 values.
2. Bars: 5–9 has 2 values; 10–14 has 9 values; 15–19 has 4 values. (correct answer)
3. Bars: 5–9 has 2 values; 10–14 has 7 values; 15–19 has 6 values.
4. Bars: 5–9 has 2 values; 10–14 has 8 values; 15–19 has 5 values.

Explanation: A histogram uses bars to show the frequency of data in specified bins along a number line. Here, the quiz scores are grouped into bins of 5 points: 5–9 includes 8 and 9 (2 values), 10–14 includes nine scores from 10 to 14, and 15–19 includes four scores from 15 to 17. The bars would visually show the tallest in the middle bin, with shorter bars on either side, indicating a peak in the 10–14 range. Choice A matches this exact count of values per bin, representing the data distribution accurately. A common misconception is including boundary values in the wrong bin, but here bins are closed on the right or as defined, correctly placing 9 in 5–9 and 15 in 15–19. Start by checking the bin scale to confirm intervals like 5–9 cover from 5 up to but not including 10 or as specified. Then, count the scores falling into each bin to ensure the bar heights reflect the frequencies.

Question 10

1. The distribution has a gap between 10 and 11 with no data values.
2. The distribution is right-skewed because there is a longer tail on the high end (up to 14). (correct answer)
3. The distribution is perfectly symmetric around 9 because 9 is the middle value.
4. The distribution is left-skewed because most values are near 14.

Explanation: A dot plot places dots for each message count on a number line, with stacks like three at 7 and two at 6, 10. The values map to positions from 5 to 14, showing a dense cluster at lower numbers and a tail stretching to 14. The shape is right-skewed with greater spread on the high end and no gaps in the data points. Choice A correctly notes the right skew due to the long tail up to 14. A common misconception is identifying skew based only on the highest value, but it's the tail's direction relative to the cluster. Verify the number line scale covers 5 to 14 appropriately. Then, count dots at each integer to ensure they total 13 days.

Question 11

1. Bars: 18.0–18.4 has 2 values; 18.5–18.9 has 4 values; 19.0–19.4 has 4 values.
2. Bars: 18.0–18.4 has 3 values; 18.5–18.9 has 4 values; 19.0–19.4 has 3 values.
3. Bars: 18.0–18.4 has 2 values; 18.5–18.9 has 5 values; 19.0–19.4 has 3 values. (correct answer)
4. Bars: 18.0–18.4 has 1 value; 18.5–18.9 has 6 values; 19.0–19.4 has 3 values.

Explanation: A histogram bins temperatures on a number line with 0.5 intervals, placing values like 18.2 and 18.4 in 18.0–18.4 (two), five in 18.5–18.9, and three in 19.0–19.4. Data maps to bars showing a peak in the middle bin and shorter adjacent bars, with spread from 18.2 to 19.3. Key features include a cluster around 18.5–18.9 and slight asymmetry. Choice A matches the precise counts per bin for accurate representation. A common misconception is misplacing decimal values across bin boundaries, but here 18.5 goes into 18.5–18.9 correctly. Check the decimal scale on the number line for bin accuracy. Then, count temperatures in each bin to confirm total of 10 measurements.

Question 12

1. There is an extreme outlier at 12.4 seconds far from the rest of the data.
2. There is a clear gap between 13.1 and 13.2 seconds with no data values.
3. The distribution is roughly symmetric with a center around about 13.2 seconds. (correct answer)
4. The distribution is strongly left-skewed because most times are near 14.0 seconds.

Explanation: A dot plot is a simple graph where each data value is represented by a dot above a number line. In this case, the sprint times are plotted as dots at their respective values, with multiple dots stacked for repeated times like the two at 12.7 and two at 13.1. The plot shows a cluster of times around 13.1 to 13.6, with the data spreading from 12.4 to 14.0 in a balanced way, forming a roughly symmetric shape around the center. Choice B correctly describes this as roughly symmetric with a center around 13.2 seconds, matching the mean and median near that value. A common misconception is thinking repeated values create gaps, but dots are placed directly at the values without spaces unless data is missing. To analyze, first check the number line scale to ensure it covers the min to max accurately. Then, count the dots at each point to verify they match the data frequencies.

Question 13

1. The median is 22 minutes, and the range is 20 minutes.
2. The median is 18 minutes, and the range is 20 minutes.
3. The median is 20 minutes, and the range is 20 minutes. (correct answer)
4. The median is 20 minutes, and the range is 15 minutes.

Explanation: This question involves a box plot of reading times for 12 students. A box plot shows five key values: minimum, Q1, median, Q3, and maximum. With 12 ordered values, the median is between the 6th and 7th values: (20+20)/2 = 20 minutes. The range is maximum minus minimum: 30-10 = 20 minutes. Box plots don't show individual data points but summarize the distribution's spread and center. A common error is confusing the interquartile range (Q3-Q1) with the full range. To create a box plot: first order the data, find the five-number summary, then draw the box from Q1 to Q3 with a line at the median.

Question 14

1. The distribution is bimodal with two equal clusters at 20 and 30 minutes and no values in between.
2. The distribution has a cluster at 25 minutes and is otherwise spread without large gaps. (correct answer)
3. The distribution has a gap from 24 to 28 minutes because there are no values in that interval.
4. The distribution has an outlier at 40 minutes that would appear far to the right.

Explanation: This question analyzes a dot plot of practice session lengths. Looking at the 13 values, three sessions were 25 minutes (creating a cluster), two were 20 minutes, two were 30 minutes, with other values spread between. The data shows no large gaps—values progress fairly steadily from 18 to 32 minutes. There's no outlier at 40 minutes, and values exist between 24 and 28 (specifically 24, 25, 26, 28). A common error is overinterpreting small gaps as significant breaks in the distribution. To identify true gaps: look for intervals where multiple consecutive values are missing, not just single missing integers.

Question 15

1. The distribution is strongly right-skewed with an outlier above 30 cm.
2. The distribution has a cluster around 16–18 cm and no large gaps. (correct answer)
3. The distribution has a clear gap between 16 and 17 cm.
4. The data are evenly spread from 14 to 21 with no clustering at any value.

Explanation: This question analyzes a dot plot of plant heights. Looking at the 12 values from 14 to 21 cm, we see three plants at 16 cm, two at 18 cm, and two at 15 cm, creating a cluster in the 16-18 cm range. The data increases steadily without large gaps—each consecutive integer from 14 to 21 is represented or close to another value. The distribution isn't strongly skewed and has no outliers above 30 cm. A common misconception is expecting perfectly even spacing for "no gaps." To identify clusters: look for values that repeat or group closely together on the number line.

Question 16

1. The median is 152.5 g, and the range is 12 g. (correct answer)
2. The median is 152.5 g, and the range is 10 g.
3. The median is 152 g, and the range is 12 g.
4. The median is 154 g, and the range is 12 g.

Explanation: This question involves a box plot of apple masses. With 10 ordered values, the median is between the 5th and 6th values: (152+153)/2 = 152.5 grams. The range is maximum minus minimum: 160-148 = 12 grams. Box plots show the five-number summary: minimum (148), Q1, median (152.5), Q3, and maximum (160). The box extends from Q1 to Q3 with a line at the median, while whiskers reach to the extremes. A common mistake is using a single middle value as the median with even sample sizes. To find the median: order all values, then average the two middle ones for even-sized datasets.

Question 17

1. A dot plot that includes an extra dot at 7.5 to show the maximum pH value.
2. A dot plot with the same counts, but the dots are placed at whole numbers only (6 and 7).
3. A dot plot with one dot at 6.6, one dot at 6.8, one dot at 7.0, and two dots at each of the other listed values.
4. A dot plot with two dots at 6.6, two dots at 6.8, two dots at 7.0, and one dot at each of the other listed values. (correct answer)

Explanation: This question tests understanding of dot plot construction. A dot plot places one dot above each data value on the number line. Counting the pH values: 6.6 appears twice, 6.8 appears twice, 7.0 appears twice, and all other values appear once. This matches option A exactly. Option B incorrectly shows single dots where there should be two. A common error is adding extra dots for emphasis or rounding values to whole numbers. To create a dot plot: mark the scale on the number line, then place one dot above the line for each occurrence of that value, stacking dots vertically when values repeat.

Question 18

1. The distribution is left-skewed because most times are near 13.6–13.7 with a few smaller times.
2. The distribution is roughly symmetric with a center near 12.9–13.0 seconds and no large gaps. (correct answer)
3. The distribution has a clear gap between 12.8 and 12.9 seconds.
4. The distribution is strongly right-skewed because there is an outlier above 15 seconds.

Explanation: This question asks about a dot plot of 100-meter dash times. A dot plot places one dot above each data value on a number line. Looking at the 15 times, they range from 12.1 to 13.7 seconds with no large gaps between consecutive values. The center (median) is the 8th value when ordered, which is 12.9 seconds. The data clusters around this middle value with roughly equal spread on both sides, making it symmetric rather than skewed. A common misconception is thinking that having more values at one end automatically means skewing, but symmetric means balanced spread around the center. To verify: count dots on each side of the median—they should be roughly equal for symmetry.

Question 19

1. 15–19: 1, 20–24: 7, 25–29: 5, 30–34: 2 (correct answer)
2. 15–19: 2, 20–24: 6, 25–29: 5, 30–34: 2
3. 15–19: 1, 20–24: 6, 25–29: 6, 30–34: 2
4. 15–19: 1, 20–24: 7, 25–29: 4, 30–34: 3

Explanation: This question requires creating a histogram with specific bins. A histogram groups data into intervals (bins) and shows the frequency with bars. For bins 15-19, 20-24, 25-29, 30-34, we count how many values fall in each range. From our data: 18 falls in 15-19 (1 value); 20, 21, 22, 22, 23, 24, 24 fall in 20-24 (7 values); 25, 26, 27, 28, 28 fall in 25-29 (5 values); 30, 32 fall in 30-34 (2 values). Answer A correctly shows these frequencies: 15-19: 1, 20-24: 7, 25-29: 5, 30-34: 2. A common error is including boundary values in the wrong bin - remember that 24 goes in the 20-24 bin, not 25-29. Always check that your total frequency equals the number of data points (1+7+5+2=15).

Question 20

1. 2–3: 3, 4–5: 5, 6–7: 4, 8–9: 3 (correct answer)
2. 2–3: 2, 4–5: 6, 6–7: 4, 8–9: 3
3. 2–3: 3, 4–5: 4, 6–7: 5, 8–9: 3
4. 2–3: 3, 4–5: 5, 6–7: 3, 8–9: 4

Explanation: This question requires creating a histogram with bins of width 2. For waiting times data: 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 8, 8, 9, we count values in each bin. For 2-3: values 2, 3, 3 give frequency 3. For 4-5: values 4, 4, 4, 5, 5 give frequency 5. For 6-7: values 6, 6, 6, 7 give frequency 4. For 8-9: values 8, 8, 9 give frequency 3. Answer A correctly shows 2-3: 3, 4-5: 5, 6-7: 4, 8-9: 3. The distribution appears roughly symmetric with a slight peak in the middle bin. A common error is forgetting that bin boundaries include both endpoints - the bin 2-3 includes both 2 and 3. Always verify your total: 3+5+4+3=15 matches our 15 data points.