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Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to measure spread with mean absolute deviation.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Arithmetic mean and absolute difference.
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
Four delivery times are 6, 8, 8, and 10 minutes. Find their mean and mean absolute deviation from the mean.
Why this math matters
Mean absolute deviation averages distances from the mean, describing variability in the original units. Compare consistency between groups using a spread measure as well as an average.
Set up the model
A useful answer starts with clear assumptions:
- All four times have equal weight.
- Use distances from the arithmetic mean, not from the median.
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 spread with mean absolute deviation
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Four delivery times are 6, 8, 8, and 10 minutes. Find their mean and mean absolute deviation from the mean.
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
mean = (6 + 8 + 8 + 10)/4 = 8 min
Find the centre before calculating distances from it.
Apply the relationship
absolute deviations = 2, 0, 0, 2 min
Distances are nonnegative even for values below the mean.
Check and interpret
MAD = (2 + 0 + 0 + 2)/4 = 1 min
The average distance from the mean is one minute.
The result
MAD = (2 + 0 + 0 + 2)/4 = 1 min
The average distance from the mean is one minute.
Common mistakes to catch
- Signed deviations sum to zero and cannot replace absolute distances.
- MAD describes spread; it is not another name for the mean.
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 the mean absolute deviation of 2, 4, 6.
Show a hint
The mean is 4; calculate three distances.
Reveal answer and explanation
4/3
The distances are 2, 0, 2, whose mean is 4/3.
Practice 2
If every original delivery time increases by 5 minutes, what happens to its MAD?
Show a hint
Both the observations and the mean shift equally.
Reveal answer and explanation
It stays 1 minute
Adding a constant changes the centre but leaves every distance from that centre unchanged.
Take the idea with you
Compare consistency between groups using a spread measure as well as an average.
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: Describe the middle half with an interquartile range
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