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Teaching video
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Grade 6 chapters and video availability01 · Read and understand
What you will learn
- Calculate mean absolute deviation for a small data set.
- 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
Find the mean absolute deviation of 2, 4, 4, and 6.
Why this math matters
Quantify how tightly values cluster around their mean with an interpretable average distance. 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.
Average distances from the mean
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Find the mean absolute deviation of 2, 4, 4, and 6.
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
Mean = (2 + 4 + 4 + 6)/4 = 4
The mean is the center used for this calculation.
Connect the parts
Absolute deviations: 2, 0, 0, 2
Measure each observation's nonnegative distance from four.
State and check the result
MAD = (2 + 0 + 0 + 2)/4 = 1
On average, observations are one unit away from the mean.
The result
MAD = (2 + 0 + 0 + 2)/4 = 1
On average, observations are one unit away from the mean.
Common mistakes to catch
- Use absolute differences before averaging.
- MAD has the original data units, not squared units.
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
Find MAD of 1, 3, and 5.
Show a hint
The mean is three; use distances two, zero, two.
Reveal answer and explanation
4/3
The total absolute distance four divided by three observations gives 4/3.
Practice 2
Why not average signed deviations instead?
Show a hint
Positive and negative differences cancel around the mean.
Reveal answer and explanation
They always sum to zero
Absolute values preserve the size of deviations so spread does not disappear by cancellation.
Take the idea with you
Quantify how tightly values cluster around their mean with an interpretable average distance.
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: Count favorable outcomes under a fair model
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