SD and Variance - Another formula (Derivation) | Statistics | Grade 11 | Math | Khan Academy

This video covers the derivation of an alternative formula for calculating variance. Starting from the fundamental definition of variance, we algebraically manipulate the expression by expanding terms and using properties of summation. This leads us to computationally simpler formulas for variance, such as (the sum of f times x squared, divided by N) minus (the mean squared). Understanding this derivation provides deeper insight into these statistical measures.

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Timestamps:
00:00 Introduction to an alternative formula for Variance
00:24 Starting with the basic Variance formula and expanding
01:57 Simplifying to reach Variance = (Sum of f_i x_i squared / N) - Mean squared
03:34 Further simplification to a second common alternative formula
04:05 Resulting formulas for Variance and Standard Deviation

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Created by
Ashish Gupta

Видео SD and Variance - Another formula (Derivation) | Statistics | Grade 11 | Math | Khan Academy канала Khan Academy India - English