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Curated by: Khan Academy India - English (13 videos)
This video explores how scaling data (multiplying each observation by a constant 'a') affects its mean, variance, and standard deviation. We first solve a specific problem where observations are doubled, observing the change in variance. Then, we'll provide a general proof to show that if a dataset has a certain mean and variance, scaling each observation by 'a' results in a new mean of 'a' times the old mean, and a new variance of 'a squared' times the old variance. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (https://www.khanacademy.org/math/ncert-class-11/xea4762213f311c5e:statistics-ncert-new/xea4762213f311c5e:variance-and-standard-deviation/e/standard_deviation_of_a_population) Timestamps: 00:00 Problem: If observations are multiplied by 2, what is the new variance? 03:35 Proof: How the mean changes when data is scaled by 'a' 05:25 Proof: How variance changes when data is scaled by 'a' (new Var = a-squared * old Var) 05:50 Conclusion on scaled data 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