Dot and Box Plot Practical

Overview

Students investigate a real-world categorical or numerical data set, then represent and interpret it using a dot plot and box plot. Building on prior learning about quartiles, medians and interquartile range, students collect or use a class data set and justify how their graphs show the distribution.

Learning intentions

• WALT plan and carry out a small statistical investigation.
• WALT construct accurate dot plots and box plots from numerical data.
• WALT calculate and use the five-number summary and interquartile range.
• WALT communicate what graphs reveal about the distribution of data.

Success criteria

• I can state the question, variable and type of data being investigated.
• I can organise data in a table and construct a correctly scaled dot plot.
• I can find the minimum, lower quartile, median, upper quartile and maximum, then use them to construct a box plot.
• I can describe the centre, spread, clusters and possible unusual values in my data.

Curriculum links

• Mathematics and Statistics — statistical investigations, data representation and interpretation.
• Mathematics and Statistics — reasoning with distributions, centre and spread.
• Mathematics and Statistics — communicating mathematical thinking and evaluating conclusions.
• Mathsteasers — higher-order questions that challenge learners to explain, compare and justify statistical representations.

Lesson structure (60 minutes)

1. 0–7 min · Hook and retrieval. Open with the hook and retrieval slides showing two contrasting data displays and ask, “Which group is more consistent, and how can you prove it?” Students discuss the difference between centre and spread, then individually recall the meanings of median, quartiles, range and IQR.

2. 7–15 min · Model the practical. Use the investigation and modelling slides to introduce the question: “What can we learn about the vehicles passing our school?” Model identifying a numerical variable, such as the age of a vehicle, and explain that a categorical variable such as colour is not suitable for a dot plot or box plot. Demonstrate ordering data, finding the five-number summary and choosing an appropriate scale.

3. 15–25 min · Plan and collect data. Give each pair the dot and box plot practical worksheet and briefly model the planning section. Students choose one agreed numerical variable, such as vehicle age, number of passengers or journey time, record the investigation question and collect or receive 30–40 data values. If leaving the room is not possible, provide the prepared class data set on the worksheet.

4. 25–38 min · Organise and calculate. Students enter their data into an ordered list or tally table, check the sample size and calculate the minimum, Q1, median, Q3, maximum, range and IQR. Support construction of the five-number summary with the Box Plot and Five-number Summary Mat. The teacher circulates, checking that students exclude the median correctly when finding Q1 and Q3 for an odd-sized data set.

5. 38–52 min · Create and interpret graphs. Students use their calculated values to construct a dot plot and box plot on the worksheet. They label axes, use an even scale and include a clear title. Students then answer interpretation questions: Where is the data concentrated? What is the typical value? Which half has greater spread? Are there clusters, gaps or possible unusual values? Use the graph-building and discussion slides to pause for a midpoint accuracy check.

6. 52–60 min · Share and assess. Pairs compare graphs with another pair and identify one similarity and one difference in their data distributions. Finish with the plenary slides and an exit response: “My data has a median of ___ and an IQR of ___. This tells me ___ about the distribution.” Collect worksheets or photograph completed work for submission.

Resources

• the dot and box plot practical slide deck
• the dot and box plot practical worksheet
• the Box Plot and Five-number Summary Mat
• Calculators or devices with a spreadsheet
• Rulers, pencils and coloured pens
• Clipboard or recording sheet for outdoor data collection
• Prepared numerical data set for use if collection is not possible
• Google Classroom submission space

Assessment

• During modelling, question students about suitable numerical variables, correct quartile methods and appropriate graph scales.
• Check each pair’s ordered data, five-number summary and graph before they begin interpretation; look for labels, scale accuracy and matching quartile positions.
• Use the exit response to assess whether students can connect the median and IQR to a statement about distribution, rather than simply reporting calculations.

Differentiation

• Provide a partially ordered data set, a number-line scale and a worked five-number-summary example for students needing support. Allow calculators or spreadsheet sorting for computation while retaining the reasoning focus.
• Use colour coding for minimum, Q1, median, Q3 and maximum, and read instructions aloud. Provide a dyslexia-friendly worksheet with a clear sans-serif font, generous spacing, short steps and uncluttered graphs.
• Pair students strategically and provide sentence starters: “The median suggests…”, “The larger IQR shows…”, and “A gap or cluster appears because…”. Offer an indoor prepared data set for students unable to collect data outdoors.
• Advanced learners can compare two groups using side-by-side box plots, decide which group is more consistent, and justify whether an apparent unusual value should be investigated further.