Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 6 chapters and video availability01 · Read and understand
What you will learn
- Compute range and an interquartile range using a stated median-of-halves convention.
- Explain your method and check what the result means in the stated situation.
Before you start
Fraction and decimal operations, whole-number factors, measurement units, and reading simple tables.
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 2, 4, 5, 7, 9, 11, find range and IQR, taking quartiles as medians of the lower and upper halves.
Why this math matters
Compare the effect of an extreme observation on broad and central measures of variability. The worked example shows how to connect the situation, its mathematical representation, and a check on the result.
Set up the model
A useful answer starts with clear assumptions:
- Use the units, grouping rules, and reference whole stated in the question.
- Treat the supplied counts and measurements as exact within the classroom model, unless an estimate or a random outcome is requested.
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.
Measure overall and middle-half spread
PausedQuestion: Start with the question. Paused.
Question
Start with the question
For 2, 4, 5, 7, 9, 11, find range and IQR, taking quartiles as 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 situation
Range = 11 − 2 = 9
Overall spread uses the smallest and largest values.
Connect the parts
Lower half 2,4,5 has Q1=4; upper half 7,9,11 has Q3=9
The stated convention fixes how quartiles are chosen.
State and check the result
IQR = 9 − 4 = 5
IQR describes the spread of the middle half and is less driven by the extremes.
The result
IQR = 9 − 4 = 5
IQR describes the spread of the middle half and is less driven by the extremes.
Common mistakes to catch
- Quartile conventions can differ; state the one used.
- Range and IQR measure different portions of spread.
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 the same convention, find IQR of 1,3,4,8,10,12.
Show a hint
Find each three-value half's median.
Reveal answer and explanation
7
Q1=3 and Q3=10, so IQR=7.
Practice 2
If the final 11 in the main data becomes 100, what happens to range and IQR?
Show a hint
Recheck extremes and each half's middle.
Reveal answer and explanation
Range becomes 98; IQR stays 5
The maximum changes greatly, but the upper-half median remains nine.
Take the idea with you
Compare the effect of an extreme observation on broad and central measures of variability.
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: Average distances from the mean
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