Measures of Variability
(Week 1-2)
Embedded Files
🧠 Explore
🎥 Watch and Learn
▶️ “Measures of Variability (Range, Mean Deviation, and Standard Deviation)”
▶️ Measures of Variability (Ungrouped Data)
▶️ “Understanding Data Dispersion”
▶️ “Finding the Standard Deviation Step-by-Step”
📊 Discover the Concept
Although both have the same mean, Section B’s scores vary more — that’s greater variability.
📈 1. Range
The simplest measure of variability.
Formula:
Range= Highest Value−Lowest Value
Example:
Heights (in cm): 140, 142, 145, 150, 152
Range=152−140=12
✅ The heights vary by 12 cm.
🧮 2. Mean Deviation (MD)
Shows the average distance of data points from the mean.
Steps:
Find the mean.
Subtract the mean from each value (find deviations).
Take absolute values.
Find the average of those deviations.
Example:
Data: 4, 6, 8
Mean = 6
Deviations: (4−6)=−2, (6−6)=0, (8−6)=2
Mean Deviation = (|−2|+|0|+|2|) ÷ 3 = 1.33
✅ Average distance from the mean is 1.33.
🧠 3. Standard Deviation (SD)
The most precise measure of variability.
✅ Standard deviation is 1.63.
🧰 Interactive Tools to Explore
🎲 GeoGebra Measures of Variability Simulation: https://www.geogebra.org/m/uhzpkayb
→ Experiment by changing data values and observing how mean deviation and SD change.
📊 Desmos Statistics Calculator: https://www.desmos.com/calculator
→ Input data sets and compute summary statistics automatically.
🧮 Calculator Soup – Mean Deviation & SD Calculator: https://www.calculatorsoup.com/calculators/statistics/standard-deviation-calculator.php
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