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Teaching video
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Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to describe the middle half with an interquartile range.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Median of an even-length ordered list.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
For the sorted data 2, 4, 5, 7, 8, 10, 12, 18, find Q1, Q3, and the interquartile range using medians of the lower and upper halves.
Why this math matters
The interquartile range measures the spread of the middle half of ordered observations. Use the IQR to discuss middle-half variation when extreme values make the full range less representative.
Set up the model
A useful answer starts with clear assumptions:
- Use the median-of-halves convention stated in the question.
- All eight observations have equal weight.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Describe the middle half with an interquartile range
PausedQuestion: Start with the question. Paused.
Question
Start with the question
For the sorted data 2, 4, 5, 7, 8, 10, 12, 18, find Q1, Q3, and the interquartile range using medians of the lower and upper halves.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
lower half: 2,4,5,7; upper half: 8,10,12,18
Split the even-length ordered list into two equally sized groups.
Apply the relationship
Q1 = (4 + 5)/2 = 4.5; Q3 = (10 + 12)/2 = 11
Take the median within each half.
Check and interpret
IQR = Q3 − Q1 = 11 − 4.5 = 6.5
This difference measures the span between the first and third quartiles.
The result
IQR = Q3 − Q1 = 11 − 4.5 = 6.5
This difference measures the span between the first and third quartiles.
Common mistakes to catch
- Find quartiles from ordered data.
- Software can use different quartile conventions, especially for short lists; state the chosen rule.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Using medians of halves, find the IQR of 1, 3, 5, 7, 9, 11.
Show a hint
Each half contains three numbers.
Reveal answer and explanation
6
Q1 = 3 and Q3 = 9, so IQR = 6.
Practice 2
If the largest value 18 in the original data becomes 100, does this convention's IQR change?
Show a hint
Recheck the two middle entries of the upper half.
Reveal answer and explanation
No; it remains 6.5
The upper-half median still averages 10 and 12; the changed extreme does not affect either quartile.
Take the idea with you
Use the IQR to discuss middle-half variation when extreme values make the full range less representative.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Scale a sample proportion to an estimated count
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