Student sheets
Three pages, twelve questions, room to work. Answers stay in a separate file.
A4 student PDFLetter student PDFDot plot worksheets
with answers.
Practice reading individual observations, counting stacked dots and drawing a dot plot from a data list. Download a ready-made worksheet with answers, or replace the data to make your own.
A complete lesson · Free to reuse
From dots to understanding.
Three short lessons on distributions, averages and histogram bins. Download student sheets separately from the worked answer key. No signup.
Worked answer key
Three pages with calculations and explanations. Print or share separately.
A4 answer key PDFLetter answer key PDFFor the teacher
Allow about 35 minutes; adapt to your learners. Prerequisites: number lines, addition and division.
Teacher notes and reuse licenseRead the lessons online ↓How to use it: print the student PDF at 100%; work through the lessons; discuss the key. The ZIP includes both paper sizes, the separate keys, original CSVs, SVG figures and teacher notes. Lessons 1–2 share completion-time data; lesson 3 uses a new waiting-time dataset.
Lesson 1 · 10 minutes
Read a dot plot
Read frequencies, describe the spread and identify two concentrations.
Count each dot once. The numbers on the horizontal axis are minutes, not frequencies.
Completion time (minutes): 2, 3, 3, 3, 4, 4, 5, 7, 8, 8, 9, 9, 9, 10. Original fictional practice values.
- How many completed tasks are shown? Explain how you counted.
- Which completion times occur most often? Give each frequency.
- What is the range? Include the unit.
- Describe the shape. Does it prove there are two different groups of people?
Show lesson 1 answers and discussion
- 1. How many completed tasks are shown? Explain how you counted.
- 14 tasks. Count all 14 dots, including repeated values.
- 2. Which completion times occur most often? Give each frequency.
- 3 and 9 minutes; each occurs 3 times.
- 3. What is the range? Include the unit.
- 10 - 2 = 8 minutes.
- 4. Describe the shape. Does it prove there are two different groups of people?
- Two separated concentrations make this a bimodal example. The plot alone does not establish two populations or explain why the peaks occur.
Bimodal describes two peaks or concentrations. Their heights need not be equal in general; this deliberately constructed sample has two equally frequent modes. Small samples and rounding can change the apparent shape.
Lesson 2 · 10 minutes
What can an average hide?
Calculate mean and median, then compare those summaries with the distribution.
Use the same completion times as lesson 1. Show your calculation before interpreting it.
Completion time (minutes): 2, 3, 3, 3, 4, 4, 5, 7, 8, 8, 9, 9, 9, 10. Original fictional practice values.
- Calculate the mean completion time. Show the total and divisor.
- Calculate the median. Which two ordered positions do you use?
- Did anyone take exactly the mean time? What does this tell you about averages?
- Write one sentence that communicates more than the mean alone.
Show lesson 2 answers and discussion
- 1. Calculate the mean completion time. Show the total and divisor.
- Total = 84 minutes; mean = 84 / 14 = 6 minutes.
- 2. Calculate the median. Which two ordered positions do you use?
- Use positions 7 and 8: 5 and 7. Median = (5 + 7) / 2 = 6 minutes.
- 3. Did anyone take exactly the mean time? What does this tell you about averages?
- No observation is 6 minutes. An average need not be an observed value; here it lies in the gap between the concentrations.
- 4. Write one sentence that communicates more than the mean alone.
- One possible answer: The 14 completion times have peaks at 3 and 9 minutes, although both mean and median are 6 minutes. Other accurate descriptions of the two concentrations are acceptable.
Mean and median answer different questions. Neither summary alone describes the two concentrations, and neither is automatically the best choice for every dataset.
Lesson 3 · 15 minutes
From dots to histogram bins
Distinguish exact-value frequencies from interval counts without changing observations.
New dataset: waiting times. Both plots use all the same waits. Bins start at 0 and have width 5 minutes; include the left edge, exclude the right edge, except the last bin includes its right edge.
Wait (minutes): 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 7, 8, 12, 17, 23. Original fictional practice values.
- How many observations are in each chart? Did grouping add or remove any?
- How many waits are from 0 up to (but not including) 5 minutes? How many are exactly 2 minutes?
- Which interval contains a wait of exactly 5 minutes?
- Could the histogram alone recover every exact wait? Explain.
Show lesson 3 answers and discussion
- 1. How many observations are in each chart? Did grouping add or remove any?
- 16 in each. Grouping changes the display, not the observations.
- 2. How many waits are from 0 up to (but not including) 5 minutes? How many are exactly 2 minutes?
- 9 are in the first interval; 3 are exactly 2 minutes. These are different questions.
- 3. Which interval contains a wait of exactly 5 minutes?
- The interval from 5 up to 10 minutes, because the left boundary is included and the right boundary is excluded.
- 4. Could the histogram alone recover every exact wait? Explain.
- No. Many different lists can have the same interval counts. Keep the raw observations if exact values matter.
Wider bins can hide gaps or combine concentrations. Do not replace a bin with repeated midpoint values and claim they are the original observations.
Adapt and share with clear attribution
The lesson text, original data and exported figures in this teaching pack are available under CC BY 4.0. Credit “ChartsAI by SupaMakers”, link to this page and the license, and indicate changes. The application source uses a separate MIT license.
These examples are constructed for practice, not research findings. We do not claim curriculum certification. The editable charts load the exact original observations; replacing their data does not rewrite this fixed lesson pack. Use the worksheet generator below for questions and answers that recalculate with your data.
Method references: NIST measures of location and NIST histogram background. The text above provides the underlying values and answers; PDF charts are images, while PDF question and answer text is selectable.
1 Choose your practice
Fictional practice data. 18 observations.
Use your own data
Select one column containing 8–40 whole-number observations.
Edit title and units
2 Preview your worksheet
Question page · Print at actual size (100%). Updating preview…
Read the data and questions as text
Books read in a month · Books. Each dot represents one observation. Repeated values remain.
Observations: 7, 2, 7, 5, 0, 1, 0, 8, 6, 2, 2, 8, 1, 3, 1, 1, 4, 1
- How many observations are shown?
- How many observations have value 4?
- What is the smallest observed value?
- What is the largest observed value?
- How many observations are greater than 4?
- Find the range of the observations.
3 Download your sheet
Question downloads always hide answers, even when you preview the key. PDFs contain high-resolution page images.
What this worksheet teaches
A dot plot places one dot above each observed value on a number line. Repeated values stack vertically. Horizontal position shows the value; stack height shows how often it occurs.
Choose a sheet, make it yours, print
- Choose reading, comparison or drawing practice. Reading and comparison have six questions; drawing has three tasks and a labelled blank chart.
- Keep the sample, generate a fresh set, or replace the data. Upload CSV or Excel, or paste spreadsheet cells. Select and check the columns before applying. The questions and worked answers are recalculated from the selected values.
- Preview and download. Print A4 or US Letter at 100%. The PDF has one question page followed by an optional answer-key page. Viewing the key does not add answers to the question page.
Use 8–40 whole-number observations between −10 and 30, spanning at most 20 units, with no more than 12 repeated values at one position. Fractions and larger datasets belong in the general dot-plot maker.
Three ready-to-print practice packs
Original fictional examples. Each PDF contains one question page and one answer-key page. Download without signing in or enabling JavaScript.
Read the chart
Count observations, read individual values and find the range. Six questions introduce position and frequency.
Compare and explain
Find median, identify all modes, compare frequencies and explain what a stack means. Six questions include worked reasoning.
Draw the chart
Draw the complete dot plot from a list, check the observation count and find the range. Three tasks include a blank axis and a separate completed graph.
A worked example with the original values
Books read in a month · Books. Observations: 7, 2, 7, 5, 0, 1, 0, 8, 6, 2, 2, 8, 1, 3, 1, 1, 4, 1. These are fictional practice values, not findings or benchmarks.
- How many observations are shown?
- 18 Count every dot once, including stacked dots.
- How many observations have value 4?
- 1 There are 1 dots directly above 4.
- What is the smallest observed value?
- 0 Read the leftmost position with a dot.
Methods and limits
Every observation is retained, including repeated values. Only the position counts used for stacking are derived. The source CSV stays in the original order.
The median uses sorted observations. For an even count, average the two middle values. The range is maximum minus minimum. Every tied mode is included; if all values occur once, this worksheet uses “no mode”.
Drawing sheets and answer keys share the same minimum, maximum and unit interval. Only the dots are hidden on the question page.
The graph and worksheet use native Apache ECharts axes and marks. Question and answer exports share the same values and scale. PDF pages contain high-resolution images; use the accessible text view or CSV downloads for selectable values and answers. There is no automated grading or curriculum-certification claim.
Common mistakes to check
- A stack of four dots at 7 means four observations of value 7; it does not mean value 4.
- Count all dots, including repeated values. The number of occupied positions is not the sample size.
- A dot plot (also called a line plot in some classrooms) is different from a line graph connecting ordered values.
Questions about using these sheets
Can I print only the questions?
Yes. Uncheck “Include a separate answer-key page” before downloading a customized PDF. For ready-made packs, print only page 1. The worksheet SVG also contains questions only.
Can I use my class data?
Yes, within the limits above. Choose “Upload a file” or “Paste data”, select the relevant columns, and review before replacing the current values. The imported data and generated files stay in your browser. Replacing a sample removes its fictional-data label.
Are the answers recalculated when data changes?
Yes. Question values, ties, comparisons and worked answers are derived from the current chart data. Changing paper size preserves the dataset. “Generate fresh data” intentionally replaces it with a new fictional practice set.
Can I share the worksheets?
Yes. Print and share these original worksheets for classroom or home practice, without an account or a watermark across the work. ChartsAI is a free, open-source project by SupaMakers.
Need a standalone graphic or more flexible data? Use the dot plot maker. Explore chart guides, number line worksheets, or bar graph worksheets and line graph worksheets..