Medians and Quartiles

Overview

Students build on prior learning about ordering data and reading dot plots to identify the median, lower quartile, upper quartile and interquartile range (IQR). They use a small, familiar dataset to explain how quartiles describe the distribution and spread of data.

Learning intentions

• WALT order a dataset and find its median.
• WALT find the lower quartile, upper quartile and interquartile range.
• WALT explain what the median and quartiles tell us about a dataset.
• WALT communicate statistical thinking using accurate mathematical language.

Success criteria

• I can arrange data from least to greatest.
• I can correctly identify the median, lower quartile and upper quartile.
• I can calculate the IQR using Q3 − Q1.
• I can explain what a quartile tells me about the data.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: applying statistical ideas through appropriately matched challenge tasks.
• Mathematics and Statistics — Additional resources for advanced learners: reasoning, explaining and justifying solutions rather than only calculating answers.
• Statistical thinking: interpreting measures of centre and spread in context, and communicating conclusions from data.

Lesson structure (60 minutes)

1. 0–7 min · Hook and prior knowledge. Teacher displays the question “How many siblings do students in our class have?” and opens the hook and prior-knowledge slides; students make a quick estimate of the median and discuss what “middle” might mean in a dataset.

2. 7–17 min · Explicit teaching. Teacher models the process using the ordered dataset 12, 13, 17, 18, 23, 24, 24, 29, 30, 33, 39: identify the median, split the remaining values into lower and upper halves, find Q1 and Q3, then calculate IQR. Students annotate the worked example on the medians and quartiles practice worksheet and explain each step to a partner.

Emphasise that the median is the middle value when there is an odd number of values. For an even number, the median is the mean of the two middle values. For this lesson, use the common convention of excluding the median when finding Q1 and Q3. Clarify that IQR describes the spread of the middle 50% of the data.

3. 17–27 min · Guided class investigation. Teacher collects or displays the class sibling data, then uses the class-data modelling slides to demonstrate ordering the values and locating the three quartiles. Students work in pairs to arrange the data, record the five-number summary on the Box Plot and Five-number Summary Mat, and compare answers with another pair.

Question prompts:

• Which value is the median, and how do you know?
• Which observations belong in the lower and upper halves?
• What would happen to the median if one very large value were added?
• Which is greater: the range or the IQR, and what does each measure?

4. 27–42 min · Pair practice and reasoning. Teacher distributes the medians and quartiles practice worksheet and circulates, checking that students order values before calculating. Students complete progressively challenging datasets, including the 11-value dataset from the worked example and an even-number dataset, then answer interpretation questions about centre and spread.

Pause after the first question for a quick “show me” check: students hold up fingers or mini-whiteboards to indicate the position of the median, Q1 and Q3. Address errors such as selecting a value that is not in the correct half or calculating the IQR as Q1 − Q3.

5. 42–52 min · Challenge and discussion. Teacher presents two datasets with the same median but different IQRs through the comparison and challenge slides. Students decide which dataset is more consistent, justify their decision using the IQR, and discuss whether the median alone gives enough information to compare the groups. Advanced learners create a dataset with a specified median and IQR, then explain whether it is unique.

6. 52–60 min · Plenary and exit check. Teacher revisits the learning intentions using the plenary and exit-question slide. Students independently complete the final question on the worksheet: for 4, 6, 7, 8, 10, 12, 15, 18, find the median, Q1, Q3 and IQR, then write one sentence describing the spread. Students self-assess each success criterion and hand in the worksheet.

Resources

• One slide deck covering the hook, worked example, class-data investigation, comparison challenge and plenary
• One-page medians and quartiles practice worksheet
• Box Plot and Five-number Summary Mat
• Mini-whiteboards or scrap paper
• Calculators for checking, not replacing, reasoning
• Class list or prepared sibling-count dataset
• Pens, rulers and highlighters

Assessment

• Listen to partner explanations during the modelling and class-data investigation, checking use of “ordered”, “lower half”, “upper half”, “median” and “IQR”.
• Use the show-me check and guided practice to identify misconceptions about odd and even datasets.
• Collect the worksheet and exit response to assess accurate calculation and interpretation. Re-teach ordering and splitting the data before the next lesson if required.

Differentiation

• Support students with a clearly spaced, dyslexia-friendly worksheet: use a sans-serif font, large print, uncluttered layout, colour-coded lower and upper halves, and one instruction per line. Read questions aloud and allow students to explain answers verbally.
• Provide a worked example, a data-ordering checklist and sentence starters such as “The median is ___ because…” and “The IQR shows that the middle 50%…”.
• Pair students strategically and allow access to a number line, calculator and concrete number cards when ordering data.
• Extend advanced learners with datasets containing repeated values or outliers, requiring them to compare median, range and IQR and justify which measure best represents the data.

Extension

• Create two different datasets containing 9 values with a median of 12 and an IQR of 8. Record the quartiles and explain how the datasets can differ while keeping these measures the same.
• Investigate how adding an extreme value changes the range, median and IQR. State which measure is most resistant to the outlier and why.