https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:problems-on-sd-and-variance/v/sd-and-variance-of-a-scaled-data-set 2025-05-30T12:59:32.180778541Z SD and Variance of a scaled data set 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. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw SD and Variance of a scaled data set 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. https://cdn.kastatic.org/ka-youtube-converted/_a-ns3QGv5Y.mp4/_a-ns3QGv5Y.mp4 366 Problems on SD and Variance https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:problems-on-sd-and-variance/v/sd-and-variance-of-a-shifted-data-set 2025-05-30T12:59:32.180778541Z SD and Variance of a shifted data set In this video, we investigate the effect of shifting data (adding a constant 'a' to each observation) on its mean, variance, and standard deviation. We will prove that while the mean shifts by the constant 'a' (i.e., new mean equals old mean plus 'a'), the variance of the dataset remains unchanged. This means the standard deviation also stays the same, as shifting data points doesn't alter their spread. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw SD and Variance of a shifted data set In this video, we investigate the effect of shifting data (adding a constant 'a' to each observation) on its mean, variance, and standard deviation. We will prove that while the mean shifts by the constant 'a' (i.e., new mean equals old mean plus 'a'), the variance of the dataset remains unchanged. This means the standard deviation also stays the same, as shifting data points doesn't alter their spread. https://cdn.kastatic.org/ka-youtube-converted/i8yZ2DrhTZc.mp4/i8yZ2DrhTZc.mp4 297 Problems on SD and Variance https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:problems-on-sd-and-variance/e/effects-of-shifting-and-scaling-the-datasets 2025-08-08T02:53:40.009522544Z Effects of shifting and scaling the datasets Effects of shifting and scaling the datasets Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:problems-on-sd-and-variance/v/sd-and-variance-finding-the-missing-entries 2025-05-30T12:59:32.180778541Z SD and Variance - finding the missing entries This video demonstrates how to find missing observations in a dataset when the mean and variance are known, along with some of the existing observations. We'll tackle a problem by setting up two equations using the formulas for mean and variance, involving the unknown entries. We then solve this system of equations to determine the values of the missing data points. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw SD and Variance - finding the missing entries This video demonstrates how to find missing observations in a dataset when the mean and variance are known, along with some of the existing observations. We'll tackle a problem by setting up two equations using the formulas for mean and variance, involving the unknown entries. We then solve this system of equations to determine the values of the missing data points. https://cdn.kastatic.org/ka-youtube-converted/Zi0ZLF92I_Y.mp4/Zi0ZLF92I_Y.mp4 373 Problems on SD and Variance https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:problems-on-sd-and-variance/e/finding-missing-entries-using-mean-and-variance 2025-08-08T02:53:40.009522544Z Finding missing entries using mean and variance Finding missing entries using mean and variance Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:problems-on-sd-and-variance/v/sd-and-variance-fixing-corrections 2025-05-30T12:59:32.180778541Z SD and Variance - fixing corrections In this video, we learn how to calculate the correct mean and standard deviation when an error in one of the recorded observations is discovered. We'll work through an example where an incorrect value was used. The process involves finding the incorrect sum of observations and incorrect sum of squares, correcting these sums by removing the effect of the erroneous value and incorporating the correct one, and then recalculating the mean and standard deviation. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw SD and Variance - fixing corrections In this video, we learn how to calculate the correct mean and standard deviation when an error in one of the recorded observations is discovered. We'll work through an example where an incorrect value was used. The process involves finding the incorrect sum of observations and incorrect sum of squares, correcting these sums by removing the effect of the erroneous value and incorporating the correct one, and then recalculating the mean and standard deviation. https://cdn.kastatic.org/ka-youtube-converted/F6r2a1j-zL0.mp4/F6r2a1j-zL0.mp4 307 Problems on SD and Variance https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:problems-on-sd-and-variance/e/correcting-mean-and-standard-deviation 2025-08-08T02:53:40.009522544Z Correcting mean and standard deviation Correcting mean and standard deviation Ashish Gupta exercise