Mathematics · Year 9 · Data Interpretation and Probability · Spring Term

Measures of Spread: Range and Interquartile Range

Students will calculate the range and interquartile range to measure the spread or consistency of data sets.

• National Curriculum Attainment Targets
• KS3: Mathematics - Statistics

About This Topic

Measures of spread, such as range and interquartile range (IQR), quantify the consistency or variability in data sets. Students calculate the range by subtracting the minimum from the maximum value, a straightforward metric that captures full extent but proves sensitive to outliers. The IQR, determined by subtracting the first quartile (Q1) from the third quartile (Q3), examines the middle 50% of ordered data, providing a stable view unaffected by extremes.

Within Year 9 Mathematics under the UK National Curriculum's KS3 Statistics strand, this topic in Data Interpretation and Probability addresses key questions like the implications for data consistency, comparisons of range versus IQR advantages and disadvantages, and outlier impacts. It strengthens prior knowledge of central tendency measures and prepares students for box plots and advanced probability analysis.

Active learning benefits this topic greatly since students work with authentic data, such as exam scores or reaction times, to compute and contrast measures firsthand. Collaborative sorting, outlier simulations, and group discussions reveal patterns intuitively, building confidence in statistical interpretation and critical thinking.

Key Questions

1. What does the range or interquartile range tell us about the consistency of a data set?
2. Compare the advantages and disadvantages of using the range versus the interquartile range.
3. Predict how an outlier might affect the range but not the interquartile range.

Learning Objectives

• Calculate the range and interquartile range for given data sets.
• Compare the advantages and disadvantages of using range versus interquartile range to describe data spread.
• Analyze the impact of outliers on the range and interquartile range of a data set.
• Explain what the range and interquartile range reveal about the consistency of a data set.

Before You Start

Ordering Data and Finding the Median

Why: Students need to be able to order data sets and find the median to calculate quartiles and the IQR.

Calculating the Mean

Why: While not directly used for range or IQR, understanding the mean reinforces the concept of data summarization and central tendency, which complements measures of spread.

Key Vocabulary

Range	The difference between the maximum and minimum values in a data set. It indicates the total spread of the data.
Interquartile Range (IQR)	The difference between the third quartile (Q3) and the first quartile (Q1) of a data set. It represents the spread of the middle 50% of the data.
Quartiles	Values that divide a data set into four equal parts. Q1 is the median of the lower half, Q2 is the overall median, and Q3 is the median of the upper half.
Outlier	A data point that is significantly different from other observations in the data set. It can be unusually high or low.

Watch Out for These Misconceptions

Common Misconception

The range is always the best measure of spread.

What to Teach Instead

Range distorts with outliers, unlike IQR which resists them. Hands-on activities where students add outliers to data sets show this visually, prompting peer discussions that clarify when each measure suits specific data types.

Common Misconception

Interquartile range includes all data points.

What to Teach Instead

IQR covers only the middle 50%, ignoring extremes. Collaborative sorting tasks help students physically isolate quartiles on number lines, reinforcing the concept through tangible manipulation and group verification.

Common Misconception

Q1 and Q3 are the same as the median.

What to Teach Instead

Median is Q2; Q1 and Q3 split the lower and upper halves. Active plotting of box plots in pairs allows students to see quartile positions clearly, correcting errors through immediate visual feedback.

Active Learning Ideas

Pair Sort: Dataset Comparison

Provide pairs with printed data sets on heights or test scores. Students order data, calculate range and IQR step-by-step, then compare spread. Pairs swap sets with neighbours to verify calculations and discuss differences.

25 min·Pairs

Small Group: Outlier Investigation

Distribute cards with data sets to small groups. Groups add or remove an outlier, recalculate range and IQR, and record changes on mini-whiteboards. Share findings in a class gallery walk.

35 min·Small Groups

Whole Class: Measure Debate

Project two data sets with outliers. Class votes on best spread measure, calculates both range and IQR together, then debates pros and cons using evidence from screenshared workings.

30 min·Whole Class

Individual: Real Data Challenge

Students collect personal data like step counts from fitness trackers. Individually order data, compute range and IQR, then annotate how outliers from one day affect results in journals.

20 min·Individual

Real-World Connections

• Sports analysts use measures of spread to compare player performance statistics. For example, they might calculate the range of points scored by a basketball player over a season to see their scoring consistency, or the IQR of their shooting percentages to understand their typical performance level.
• Financial analysts examine stock market data to assess risk and volatility. The range of a stock's price over a month can show its extreme fluctuations, while the IQR can indicate its typical trading behavior, helping investors make informed decisions.

Assessment Ideas

Quick Check

Provide students with two small data sets, one with an obvious outlier. Ask them to calculate the range and IQR for both sets. Then, pose the question: 'Which measure, range or IQR, better represents the typical spread of data in each set and why?'

Discussion Prompt

Present a scenario: 'A teacher is comparing the test scores of two classes. Class A has scores ranging from 45 to 95, with an IQR of 15. Class B has scores ranging from 65 to 85, with an IQR of 20.' Facilitate a discussion using prompts like: 'What do these measures tell you about the consistency of scores in each class? Which class has more consistent scores overall? Why might the range be misleading here?'

Exit Ticket

Give each student a data set. Ask them to calculate the range and IQR. On the back, have them write one sentence explaining what the IQR of their data set signifies and one sentence about how an outlier would affect the range but not the IQR.

Frequently Asked Questions

What is the difference between range and interquartile range?

Range measures full data spread from minimum to maximum, easy to compute but outlier-sensitive. IQR focuses on middle 50% spread between Q1 and Q3, more reliable for skewed data. Students benefit from comparing both on familiar sets like class ages to grasp reliability in real contexts.

How do outliers affect range and IQR?

Outliers greatly increase range by shifting min or max, but IQR remains stable as it excludes extremes. Activities simulating outliers, like altering sports scores, let students quantify effects and choose appropriate measures for robust analysis.

How can active learning help students understand measures of spread?

Active methods like sorting physical data cards or simulating outliers in groups make abstract calculations concrete. Students see range inflate while IQR holds steady, sparking discussions that solidify comparisons. This builds deeper insight than worksheets alone, aligning with KS3 emphasis on practical statistics.

Why compare advantages of range versus IQR?

Range offers simplicity and full span view, ideal for symmetric data without outliers. IQR provides consistency against extremes, better for real-world variability. Classroom debates with student-generated data highlight contexts, fostering judgement skills for GCSE statistics.