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6th grade questions for box plots,frequency table,histogram, and dot plot
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Here are sets of 6th‑grade level problems (with answers) organized by topic: dot plots, frequency tables, histograms, and box plots. Use these for class practice, quizzes, or homework. Each problem includes a short answer key and a brief explanation when needed.
Guidance for students: show work, draw plots to scale, label axes and bins, and write units if given.
DOT PLOTS (6 problems)
1) Data: test scores (out of 10) for 12 students:
7, 8, 6, 7, 9, 8, 7, 10, 6, 8, 7, 9
a) Make a dot plot.
b) What is the mode? median? range?
Answers:
a) Dot plot with counts above each value (6:••, 7:••••, 8:•••, 9:••, 10:•).
b) Mode = 7; median = average of 6th and 7th numbers when sorted: sorted = 6,6,7,7,7,7,8,8,8,9,9,10 → 6th=7,7th=8 → median = 7.5; range = 10−6 = 4.
2) Data: number of books read by 15 classmates this month:
2, 3, 3, 1, 4, 2, 3, 0, 1, 2, 5, 2, 3, 1, 2
a) Make a dot plot.
b) Which value occurs most often?
Answer:
a) Dot plot with counts: 0:•, 1:•••, 2:•••••, 3:••••, 4:•, 5:•.
b) Most often = 2.
3) Given dot plot (students draw): x-axis 0–6 with dots: 0(1), 1(2), 2(4), 3(5), 4(3), 5(2), 6(1).
a) Total number of data points? b) Median?
Answers:
a) Total = 1+2+4+5+3+2+1 = 18.
b) Median = average of 9th and 10th data values. Cumulative counts: 1,3,7,12 → 9th and 10th are both at value 3 → median = 3.
4) Create a dot plot for the following times (minutes) students spent on homework: 15, 20, 15, 25, 30, 20, 15, 10.
Find mean and range.
Answers:
Dot plot as drawn. Mean = (15+20+15+25+30+20+15+10)/8 = 150/8 = 18.75 min. Range = 30−10 = 20.
5) Use a dot plot to compare two small data sets (teacher provides blank chart). Which set is more spread out? (Teacher to supply numbers)
(Example answer explanation)
Look at extent from smallest to largest; larger spread means more spread out.
6) One dot plot shows heights (in inches): 54(2), 55(3), 56(4), 57(1). What percent of students have height 56?
Answer:
Total = 2+3+4+1 = 10. Percent with 56 = 4/10 = 40%.
FREQUENCY TABLES (6 problems)
7) Raw data: shoe sizes for 12 students: 5, 6, 5, 7, 6, 6, 8, 5, 7, 6, 5, 6.
a) Make a frequency table.
b) Which shoe size is most common?
Answer:
Frequency table: size 5:4, 6:5, 7:2, 8:1. Most common = 6.
8) Data: ages of pets at a shelter: 1, 2, 3, 2, 4, 1, 3, 2, 5, 1.
a) Make frequency and relative frequency table.
b) What fraction of pets are 2 years old?
Answers:
Frequency: 1:3, 2:3, 3:2, 4:1, 5:1. Relative frequency (out of 10): 1:0.30, 2:0.30, 3:0.20, 4:0.10, 5:0.10. Fraction 2-year-old = 3/10.
9) Grouped frequency table: test scores (0–100) for 20 students will be grouped in bins of width 10 (0–9, 10–19, …, 90–100). Teacher supplies raw list. Student must create table and fill counts.
(Example answer format)
Counts per interval.
10) Given frequency table:
Value Frequency
2 3
3 5
4 2
5 4
a) How many data points total?
b) Find the mode.
Answers:
a) Total = 3+5+2+4 = 14. b) Mode = 3 (highest frequency).
11) From a frequency table, create a cumulative frequency column and use it to find the median. Example:
Value Freq
10 2
20 4
30 3
40 1
Total 10
Median is the 5th and 6th values → both in 20 bin → median ≈ 20.
12) A survey: favorite fruit counts: apples 12, bananas 8, oranges 5, grapes 5. Build a table and state which fruit ties for least favorite.
Answer:
Table as given. Least favorite: oranges and grapes (tie with 5 each).
HISTOGRAMS (6 problems)
13) Create a histogram from this grouped data (bins 0–9,10–19,20–29,...): counts: 0–9:2, 10–19:6, 20–29:8, 30–39:4.
a) Draw histogram.
b) Which bin has the highest frequency?
Answer:
Draw bars with heights 2,6,8,4. Highest = 20–29.
14) Data: weights of 15 apples (ounces) grouped as:
100–109: 2
110–119: 5
120–129: 6
130–139: 2
Sketch the histogram and estimate which weight range contains the median apple.
Answer:
Total = 15; median is 8th value. Cumulative: 2,7,13 → 8th in 120–129 bin → median in 120–129.
15) Convert this frequency table into a histogram: scores 0–9:1, 10–19:3, 20–29:6, 30–39:4, 40–49:1. Which bins should be labeled on x-axis? (Answer)
Label x-axis by ranges (0–9, 10–19, …). Heights match frequencies.
16) Explain difference between bar graph and histogram. (Short answer)
Answer:
Histogram groups numeric continuous data into adjacent intervals (bars touch). Bar graph compares categories (bars separated).
17) Given a histogram with bin heights 3, 5, 9, 3 and bin widths all 10, estimate total data points and state which bin is smallest.
Answer:
Total = 3+5+9+3 = 20. Smallest bins are first and last (3 each).
18) Data set (teacher gives raw numbers). Student must choose appropriate bin width, make grouped frequency table, and draw histogram. (Use teacher-provided numbers; example solution shows chosen bins and counts.)
BOX PLOTS (6 problems)
19) Data: ages of 9 kids at a club: 8, 9, 9, 10, 11, 12, 12, 13, 14.
a) Find five-number summary (min, Q1, median, Q3, max).
b) Draw box plot.
Answers:
Sorted: 8,9,9,10,11,12,12,13,14. Min=8, max=14, median=11 (5th), Q1 = median of lower half (8,9,9,10) → average of middle two (9 and 9) = 9, Q3 = median of upper half (12,12,13,14) → average of middle two (12 and 12) = 12. Five-number summary: 8, 9, 11, 12, 14.
20) Given five-number summary: min=20, Q1=24, median=27, Q3=33, max=40. Draw box plot and find IQR and check if 10 is an outlier using 1.5×IQR rule.
Answers:
IQR = 33−24 = 9. 1.5×IQR = 13.5. Lower fence = 24 − 13.5 = 10.5; upper fence = 33 + 13.5 = 46.5. 10 is below 10.5, so 10 would be an outlier.
21) Data: 6, 7, 8, 15, 20, 22, 23, 24
a) Find median, Q1, Q3.
b) Is 30 an outlier?
Answers:
Sorted already. n=8, median = average of 4th and 5th: (15+20)/2 = 17.5. Lower half: 6,7,8,15 → Q1 = average of 7 and 8 = 7.5. Upper half: 20,22,23,24 → Q3 = average of 22 and 23 = 22.5. IQR = 22.5−7.5 = 15. 1.5×IQR = 22.5. Upper fence = 22.5 + 22.5 = 45. So 30 is not an outlier.
22) Two box plots side-by-side show Test A (median 78, IQR 10) and Test B (median 82, IQR 14). Which test has more spread? Which has higher typical score?
Answer:
Test B has more spread (larger IQR). Test B also has higher typical score (higher median 82 vs 78).
23) Construct a box plot from raw data: 3, 5, 7, 8, 9, 10, 12, 13, 18.
Provide five-number summary and draw plot.
Answers:
Sorted data same. n=9 median=8 (5th). Lower half: 3,5,7,8 → Q1 = average of 5 and 7 = 6. Upper half: 9,10,12,13,18 → wait, correct upper half should be 9,10,12,13,18? For n odd, exclude median: lower 3,5,7,8 → Q1=6; upper 9,10,12,13,18 → Q3 = median of upper half (12) = 12. Five-number: min 3, Q1 6, median 8, Q3 12, max 18.
MIXED REVIEW (6 problems)
24) You have raw data for 20 students' minutes of screen time. Make a frequency table (group into 0–29,30–59,60–89,90–119), draw histogram, then make a box plot. (Teacher provides numbers; solution should show grouping, histogram counts, and five-number summary.)
25) Which plot is best for showing individual repeated values clearly: dot plot, histogram, or box plot? Explain.
Answer:
Dot plot — it shows each data point and repeats as stacked dots.
26) Given two data sets A and B with same median but A has a much larger IQR. What does this tell you?
Answer:
Both have same center, but A is more spread out; its middle 50% of values has greater variability.
27) The frequency table of shoe sizes shows a mode of 7 and mean of 7.1. Does the mean have to equal the mode? Explain using context.
Answer:
No. Mean is average and can differ from mode (most common value).
28) Create a histogram from this table and then convert it to a relative frequency histogram: bin counts 4, 6, 10 out of total 20. What are relative heights?
Answer:
Relative heights = 4/20 = 0.20, 6/20 = 0.30, 10/20 = 0.50.
29) A box plot shows a long whisker to the right and a cluster of the box near the left. What can you say about skewness?
Answer:
The distribution is right-skewed (long tail on the right).
Answer key notes and teacher tips
- For Q1–Q6 (dot plots) students should stack dots above each value.
- For frequency tables include columns for value/bin, frequency, and optional relative and cumulative frequency.
- Histograms require contiguous bins for numeric data; bars touch.
- For box plots teach the 1.5×IQR rule for outliers; when n is odd exclude median when finding Q1 and Q3.
- Keep numbers small and whole for 6th grade; avoid complex decimals unless practicing mean.
If you’d like, I can:
- Format these into printable worksheet pages,
- Create answer sheets with full step-by-step solutions,
- Provide teacher versions with blanks for students and an escalation in difficulty. Which would you prefer?
Guidance for students: show work, draw plots to scale, label axes and bins, and write units if given.
DOT PLOTS (6 problems)
1) Data: test scores (out of 10) for 12 students:
7, 8, 6, 7, 9, 8, 7, 10, 6, 8, 7, 9
a) Make a dot plot.
b) What is the mode? median? range?
Answers:
a) Dot plot with counts above each value (6:••, 7:••••, 8:•••, 9:••, 10:•).
b) Mode = 7; median = average of 6th and 7th numbers when sorted: sorted = 6,6,7,7,7,7,8,8,8,9,9,10 → 6th=7,7th=8 → median = 7.5; range = 10−6 = 4.
2) Data: number of books read by 15 classmates this month:
2, 3, 3, 1, 4, 2, 3, 0, 1, 2, 5, 2, 3, 1, 2
a) Make a dot plot.
b) Which value occurs most often?
Answer:
a) Dot plot with counts: 0:•, 1:•••, 2:•••••, 3:••••, 4:•, 5:•.
b) Most often = 2.
3) Given dot plot (students draw): x-axis 0–6 with dots: 0(1), 1(2), 2(4), 3(5), 4(3), 5(2), 6(1).
a) Total number of data points? b) Median?
Answers:
a) Total = 1+2+4+5+3+2+1 = 18.
b) Median = average of 9th and 10th data values. Cumulative counts: 1,3,7,12 → 9th and 10th are both at value 3 → median = 3.
4) Create a dot plot for the following times (minutes) students spent on homework: 15, 20, 15, 25, 30, 20, 15, 10.
Find mean and range.
Answers:
Dot plot as drawn. Mean = (15+20+15+25+30+20+15+10)/8 = 150/8 = 18.75 min. Range = 30−10 = 20.
5) Use a dot plot to compare two small data sets (teacher provides blank chart). Which set is more spread out? (Teacher to supply numbers)
(Example answer explanation)
Look at extent from smallest to largest; larger spread means more spread out.
6) One dot plot shows heights (in inches): 54(2), 55(3), 56(4), 57(1). What percent of students have height 56?
Answer:
Total = 2+3+4+1 = 10. Percent with 56 = 4/10 = 40%.
FREQUENCY TABLES (6 problems)
7) Raw data: shoe sizes for 12 students: 5, 6, 5, 7, 6, 6, 8, 5, 7, 6, 5, 6.
a) Make a frequency table.
b) Which shoe size is most common?
Answer:
Frequency table: size 5:4, 6:5, 7:2, 8:1. Most common = 6.
8) Data: ages of pets at a shelter: 1, 2, 3, 2, 4, 1, 3, 2, 5, 1.
a) Make frequency and relative frequency table.
b) What fraction of pets are 2 years old?
Answers:
Frequency: 1:3, 2:3, 3:2, 4:1, 5:1. Relative frequency (out of 10): 1:0.30, 2:0.30, 3:0.20, 4:0.10, 5:0.10. Fraction 2-year-old = 3/10.
9) Grouped frequency table: test scores (0–100) for 20 students will be grouped in bins of width 10 (0–9, 10–19, …, 90–100). Teacher supplies raw list. Student must create table and fill counts.
(Example answer format)
Counts per interval.
10) Given frequency table:
Value Frequency
2 3
3 5
4 2
5 4
a) How many data points total?
b) Find the mode.
Answers:
a) Total = 3+5+2+4 = 14. b) Mode = 3 (highest frequency).
11) From a frequency table, create a cumulative frequency column and use it to find the median. Example:
Value Freq
10 2
20 4
30 3
40 1
Total 10
Median is the 5th and 6th values → both in 20 bin → median ≈ 20.
12) A survey: favorite fruit counts: apples 12, bananas 8, oranges 5, grapes 5. Build a table and state which fruit ties for least favorite.
Answer:
Table as given. Least favorite: oranges and grapes (tie with 5 each).
HISTOGRAMS (6 problems)
13) Create a histogram from this grouped data (bins 0–9,10–19,20–29,...): counts: 0–9:2, 10–19:6, 20–29:8, 30–39:4.
a) Draw histogram.
b) Which bin has the highest frequency?
Answer:
Draw bars with heights 2,6,8,4. Highest = 20–29.
14) Data: weights of 15 apples (ounces) grouped as:
100–109: 2
110–119: 5
120–129: 6
130–139: 2
Sketch the histogram and estimate which weight range contains the median apple.
Answer:
Total = 15; median is 8th value. Cumulative: 2,7,13 → 8th in 120–129 bin → median in 120–129.
15) Convert this frequency table into a histogram: scores 0–9:1, 10–19:3, 20–29:6, 30–39:4, 40–49:1. Which bins should be labeled on x-axis? (Answer)
Label x-axis by ranges (0–9, 10–19, …). Heights match frequencies.
16) Explain difference between bar graph and histogram. (Short answer)
Answer:
Histogram groups numeric continuous data into adjacent intervals (bars touch). Bar graph compares categories (bars separated).
17) Given a histogram with bin heights 3, 5, 9, 3 and bin widths all 10, estimate total data points and state which bin is smallest.
Answer:
Total = 3+5+9+3 = 20. Smallest bins are first and last (3 each).
18) Data set (teacher gives raw numbers). Student must choose appropriate bin width, make grouped frequency table, and draw histogram. (Use teacher-provided numbers; example solution shows chosen bins and counts.)
BOX PLOTS (6 problems)
19) Data: ages of 9 kids at a club: 8, 9, 9, 10, 11, 12, 12, 13, 14.
a) Find five-number summary (min, Q1, median, Q3, max).
b) Draw box plot.
Answers:
Sorted: 8,9,9,10,11,12,12,13,14. Min=8, max=14, median=11 (5th), Q1 = median of lower half (8,9,9,10) → average of middle two (9 and 9) = 9, Q3 = median of upper half (12,12,13,14) → average of middle two (12 and 12) = 12. Five-number summary: 8, 9, 11, 12, 14.
20) Given five-number summary: min=20, Q1=24, median=27, Q3=33, max=40. Draw box plot and find IQR and check if 10 is an outlier using 1.5×IQR rule.
Answers:
IQR = 33−24 = 9. 1.5×IQR = 13.5. Lower fence = 24 − 13.5 = 10.5; upper fence = 33 + 13.5 = 46.5. 10 is below 10.5, so 10 would be an outlier.
21) Data: 6, 7, 8, 15, 20, 22, 23, 24
a) Find median, Q1, Q3.
b) Is 30 an outlier?
Answers:
Sorted already. n=8, median = average of 4th and 5th: (15+20)/2 = 17.5. Lower half: 6,7,8,15 → Q1 = average of 7 and 8 = 7.5. Upper half: 20,22,23,24 → Q3 = average of 22 and 23 = 22.5. IQR = 22.5−7.5 = 15. 1.5×IQR = 22.5. Upper fence = 22.5 + 22.5 = 45. So 30 is not an outlier.
22) Two box plots side-by-side show Test A (median 78, IQR 10) and Test B (median 82, IQR 14). Which test has more spread? Which has higher typical score?
Answer:
Test B has more spread (larger IQR). Test B also has higher typical score (higher median 82 vs 78).
23) Construct a box plot from raw data: 3, 5, 7, 8, 9, 10, 12, 13, 18.
Provide five-number summary and draw plot.
Answers:
Sorted data same. n=9 median=8 (5th). Lower half: 3,5,7,8 → Q1 = average of 5 and 7 = 6. Upper half: 9,10,12,13,18 → wait, correct upper half should be 9,10,12,13,18? For n odd, exclude median: lower 3,5,7,8 → Q1=6; upper 9,10,12,13,18 → Q3 = median of upper half (12) = 12. Five-number: min 3, Q1 6, median 8, Q3 12, max 18.
MIXED REVIEW (6 problems)
24) You have raw data for 20 students' minutes of screen time. Make a frequency table (group into 0–29,30–59,60–89,90–119), draw histogram, then make a box plot. (Teacher provides numbers; solution should show grouping, histogram counts, and five-number summary.)
25) Which plot is best for showing individual repeated values clearly: dot plot, histogram, or box plot? Explain.
Answer:
Dot plot — it shows each data point and repeats as stacked dots.
26) Given two data sets A and B with same median but A has a much larger IQR. What does this tell you?
Answer:
Both have same center, but A is more spread out; its middle 50% of values has greater variability.
27) The frequency table of shoe sizes shows a mode of 7 and mean of 7.1. Does the mean have to equal the mode? Explain using context.
Answer:
No. Mean is average and can differ from mode (most common value).
28) Create a histogram from this table and then convert it to a relative frequency histogram: bin counts 4, 6, 10 out of total 20. What are relative heights?
Answer:
Relative heights = 4/20 = 0.20, 6/20 = 0.30, 10/20 = 0.50.
29) A box plot shows a long whisker to the right and a cluster of the box near the left. What can you say about skewness?
Answer:
The distribution is right-skewed (long tail on the right).
Answer key notes and teacher tips
- For Q1–Q6 (dot plots) students should stack dots above each value.
- For frequency tables include columns for value/bin, frequency, and optional relative and cumulative frequency.
- Histograms require contiguous bins for numeric data; bars touch.
- For box plots teach the 1.5×IQR rule for outliers; when n is odd exclude median when finding Q1 and Q3.
- Keep numbers small and whole for 6th grade; avoid complex decimals unless practicing mean.
If you’d like, I can:
- Format these into printable worksheet pages,
- Create answer sheets with full step-by-step solutions,
- Provide teacher versions with blanks for students and an escalation in difficulty. Which would you prefer?
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