Скачать или смотреть SD and Variance - Shortcut method (Derivation)| Statistics | Grade 11 | Math | Khan Academy

This video explains the derivation of the shortcut method, also known as the step-deviation method, for calculating variance and standard deviation. We introduce the concept of step-deviations (y sub i equals (x sub i minus A) divided by h) to simplify calculations. We'll derive the relationship between the mean of the original data and the mean of the step-deviations, and then show how their variances are related. This leads to the useful shortcut formula for standard deviation.

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (https://www.khanacademy.org/math/ncer...)

Timestamps:
00:00 Introduction to the shortcut (step-deviation) method derivation
00:20 Defining step-deviations (y_i) and relating original data (x_i) to y_i
00:59 Deriving the relationship between the mean of x and mean of y
02:45 Deriving the relationship between variance of x and variance of y (Var(x) = h-squared * Var(y))
04:30 Final shortcut formula for Standard Deviation of x

Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month.
Support Us: https://india.khanacademy.org/donate

Created by
Ashish Gupta