https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/variance-standard-deviation-population/v/range-variance-and-standard-deviation-as-measures-of-dispersion 2022-11-16T04:22:43.7414897Z Measures of spread: range, variance & standard deviation Range, variance, and standard deviation all measure the spread or variability of a data set in different ways. The range is easy to calculate—it's the difference between the largest and smallest data points in a set. Standard deviation is the square root of the variance. Standard deviation is a measure of how spread out the data is from its mean. Sal Khan video https://cdn.kastatic.org/googleusercontent/F7u5R7KncKAiNkwZK0i3DTxYrCpwFG1YuVhgwHtYHWUsRNB9rlgxRnkqR4onfr1ex44Yc9FmnodarnP_ZcWwhCg Measures of spread: range, variance & standard deviation Range, variance, and standard deviation all measure the spread or variability of a data set in different ways. The range is easy to calculate—it's the difference between the largest and smallest data points in a set. Standard deviation is the square root of the variance. Standard deviation is a measure of how spread out the data is from its mean. https://cdn.kastatic.org/ka-youtube-converted/E4HAYd0QnRc.mp4/E4HAYd0QnRc.mp4 754 Variance and standard deviation https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/variance-standard-deviation-population/v/variance-of-a-population 2022-11-16T04:22:43.7414897Z Variance of a population Population variance is a measure of how spread out a group of data points is. Specifically, it quantifies the average squared deviation from the mean. So, if all data points are very close to the mean, the variance will be small; if data points are spread out over a wide range, the variance will be larger. Sal Khan video https://cdn.kastatic.org/googleusercontent/sUTdtwwuC1IpaLnXVdusUnRLzWhWCnHJCcTIXiNLI9srUre3T-5q2ppvPaCIlm2ObKKXq0VHt-CtWCHZZbp74RuX Variance of a population Population variance is a measure of how spread out a group of data points is. Specifically, it quantifies the average squared deviation from the mean. So, if all data points are very close to the mean, the variance will be small; if data points are spread out over a wide range, the variance will be larger. https://cdn.kastatic.org/ka-youtube-converted/dvoHB9djouc.mp4/dvoHB9djouc.mp4 485 Variance and standard deviation https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/variance-standard-deviation-population/v/population-standard-deviation 2022-11-16T04:22:43.7414897Z Population standard deviation The population standard deviation is a measure of how much variation there is among individual data points in a population. It's a way of quantifying how spread out the data is from its mean. A small standard deviation means that the data points are generally close to the mean, while a large standard deviation means that the data is more dispersed. Sal Khan video https://cdn.kastatic.org/googleusercontent/k_NEs5TMoK3h4hVCq-NdJuWu-m-zezkYHDWD0101WVc341lk1KnLMTZvt4JStlTH9LZa5rmJUjYXGNGJ6f2meQb1Jw Population standard deviation The population standard deviation is a measure of how much variation there is among individual data points in a population. It's a way of quantifying how spread out the data is from its mean. A small standard deviation means that the data points are generally close to the mean, while a large standard deviation means that the data is more dispersed. https://cdn.kastatic.org/ka-youtube-converted/PWiWkqHmum0.mp4/PWiWkqHmum0.mp4 485 Variance and standard deviation https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:variance-and-standard-deviation/v/standard-deviation-and-variance-continuous 2025-05-30T12:59:32.180778541Z Standard deviation and Variance (continuous) In this video, we learn how to calculate the mean, variance, and standard deviation for continuous grouped data. We'll go through a detailed example, starting from finding mid-points, calculating the mean, then the deviations from the mean, their squares, and the sum of their products with frequencies to find the variance. Finally, we'll take the square root of the variance to get the standard deviation. The complete step-by-step method is also explained. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Standard deviation and Variance (continuous) In this video, we learn how to calculate the mean, variance, and standard deviation for continuous grouped data. We'll go through a detailed example, starting from finding mid-points, calculating the mean, then the deviations from the mean, their squares, and the sum of their products with frequencies to find the variance. Finally, we'll take the square root of the variance to get the standard deviation. The complete step-by-step method is also explained. https://cdn.kastatic.org/ka-youtube-converted/lh3t60hjII8.mp4/lh3t60hjII8.mp4 384 Variance and standard deviation https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:variance-and-standard-deviation/e/standard-deviation-and-variance-continuous 2025-08-04T10:19:49.801518088Z Standard deviation and Variance (continuous) Standard deviation and Variance (continuous) Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:variance-and-standard-deviation/v/sd-and-variance-another-formula-derivation 2025-05-30T12:59:32.180778541Z SD and Variance - Another formula (Derivation) 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. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw SD and Variance - Another formula (Derivation) 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. https://cdn.kastatic.org/ka-youtube-converted/IO63JMNCQwQ.mp4/IO63JMNCQwQ.mp4 262 Variance and standard deviation https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:variance-and-standard-deviation/v/sd-and-variance-another-formula-application 2025-05-30T12:59:32.180778541Z SD and Variance - Another formula (Application) In this video, we demonstrate how to apply the alternative formula for calculating standard deviation. We'll work through an example with discrete data, constructing a table to find N (total frequency), the sum of (f times x), and the sum of (f times x squared). Then, we'll plug these values into the alternative formula to efficiently find the standard deviation. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw SD and Variance - Another formula (Application) In this video, we demonstrate how to apply the alternative formula for calculating standard deviation. We'll work through an example with discrete data, constructing a table to find N (total frequency), the sum of (f times x), and the sum of (f times x squared). Then, we'll plug these values into the alternative formula to efficiently find the standard deviation. https://cdn.kastatic.org/ka-youtube-converted/oLaJzko9JOI.mp4/oLaJzko9JOI.mp4 289 Variance and standard deviation https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:variance-and-standard-deviation/e/sd-and-variance-another-formula 2025-08-04T10:19:49.801518088Z SD and Variance - Another formula SD and Variance - Another formula Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:variance-and-standard-deviation/v/sd-and-variance-shortcut-method-derivation 2025-05-30T12:59:32.180778541Z SD and Variance - Shortcut method (Derivation) 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. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw SD and Variance - Shortcut method (Derivation) 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. https://cdn.kastatic.org/ka-youtube-converted/DLpOO79QLTQ.mp4/DLpOO79QLTQ.mp4 296 Variance and standard deviation https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:variance-and-standard-deviation/v/sd-and-variance-shortcut-method-application 2025-05-30T12:59:32.180778541Z SD and Variance - Shortcut method (Application) In this video, we apply the shortcut (step-deviation) method to calculate the mean, variance, and standard deviation for continuous grouped data. We'll work through an example, choosing an assumed mean (A) and class size (h) to simplify our data into 'y' values. We then compute the necessary sums and use the shortcut formulas to find the mean, variance, and standard deviation. This method can significantly reduce calculation complexity. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw SD and Variance - Shortcut method (Application) In this video, we apply the shortcut (step-deviation) method to calculate the mean, variance, and standard deviation for continuous grouped data. We'll work through an example, choosing an assumed mean (A) and class size (h) to simplify our data into 'y' values. We then compute the necessary sums and use the shortcut formulas to find the mean, variance, and standard deviation. This method can significantly reduce calculation complexity. https://cdn.kastatic.org/ka-youtube-converted/-oZWB33PnEM.mp4/-oZWB33PnEM.mp4 356 Variance and standard deviation https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:statistics-ncert-new/x0419e5b3b578592a:variance-and-standard-deviation/e/sd-and-variance-step-deviation-method 2025-08-04T10:19:49.801518088Z SD and Variance - step deviation method SD and Variance - step deviation method SD and Variance - step deviation method exercise https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/variance-standard-deviation-population/a/introduction-to-standard-deviation 2023-02-22T03:54:13.328982673Z The idea of spread and standard deviation See how distributions that are more spread out have a greater standard deviation. article https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/variance-standard-deviation-population/a/calculating-standard-deviation-step-by-step 2021-07-03T00:16:52Z Calculating standard deviation step by step article https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/variance-standard-deviation-population/e/standard_deviation_of_a_population 2025-03-01T15:52:37.13987578Z Standard deviation of a population Calculate the standard deviation of a population. exercise https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/variance-standard-deviation-population/a/concept-check-standard-deviation 2024-11-04T03:24:04.544183802Z Concept check: Standard deviation Six questions that will help you understand standard deviation more deeply. article