Key Differences Between Range, Variance, and Standard Deviation
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Range:
- What It Is: The range shows how spread out the numbers are by looking at the biggest and smallest numbers in a dataset.
- How to Calculate It:
- Range = Maximum value - Minimum value
- Example: For the numbers {3, 7, 2}, the range is:
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Variance:
- What It Is: Variance tells us how much the numbers in a dataset differ from the average (mean).
- How to Calculate It:
- Variance = (The average of the square differences from the mean)
- Example: For the numbers {2, 4, 6}:
- First, find the mean: Mean = 4.
- Then, calculate variance:
- Variance = ( (2 - 4)² + (4 - 4)² + (6 - 4)² ) ÷ 3
- Variance = (4 + 0 + 4) ÷ 3 = 8 ÷ 3 ≈ 2.67.
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Standard Deviation:
- What It Is: Standard deviation is like variance but gives us a better idea of how spread out the numbers are in the same size as the original numbers.
- How to Calculate It:
- Standard Deviation = The square root of the variance.
- Example: From the previous variance example:
- Standard Deviation = √2.67 ≈ 1.63.
Each of these measures helps us understand how much the numbers in our data can vary.