how to calculate the variance for grouped data?
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Formula for Sample Variance The variance of a sample for grouped data is: s2 = ∑ f (m − x̅)2 / n − 1.
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Portfolio variance is calculated by multiplying the squared weight of each security by its corresponding variance and adding twice the weighted average weight multiplied by the covariance of all individual security pairs.
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['Work out the Mean (the simple average of the numbers)', 'Then for each number: subtract the Mean and square the result.', 'Then work out the mean of those squared differences.', 'Take the square root of that and we are done!']
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You calculate the percent variance by subtracting the benchmark number from the new number and then dividing that result by the benchmark number. In this example, the calculation looks like this: (150-120)/120 = 25%.
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If you square and average the difference between each number and the mean, the result is 82.5. To figure out the variance, subtract 82.5 from the mean, which is 5.5 and then divide by N, which is the value of numbers, (in this case 10) minus 1. The result is a variance of about 9.17.
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['Summary. The Excel VAR function estimates the variance of a sample of data. ... ', 'Get variation of a sample.', 'Computed variance.', '=VAR (number1, [number2], ...)', 'number1 - First number or reference. number2 - [optional] Second number or reference.', 'The VAR function estimates the variance for a sample of data.']
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['Calculate the mean (simple average of the numbers).', 'For each number: Subtract the mean. Square the result.', 'Calculate the mean of those squared differences. ... ', 'Take the square root of that to obtain the population standard deviation.']
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To figure out the variance, subtract 82.5 from the mean, which is 5.5 and then divide by N, which is the value of numbers, (in this case 10) minus 1. The result is a variance of about 9.17. Standard deviation is the square root of the variance so that the standard deviation would be about 3.03.
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To compute the pooled SD from several groups, calculate the difference between each value and its group mean, square those differences, add them all up (for all groups), and divide by the number of df, which equals the total sample size minus the number of groups. That value is the residual mean square of ANOVA.
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To calculate sales volume variance, subtract the budgeted quantity sold from the actual quantity sold and multiply by the standard selling price. For example, if a company expected to sell 20 widgets at $100 a piece but only sold 15, the variance is 5 multiplied by $100, or $500.
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['Each group sample is drawn from a normally distributed population.', 'All populations have a common variance.', 'All samples are drawn independently of each other.', 'Within each sample, the observations are sampled randomly and independently of each other.', 'Factor effects are additive.']
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You calculate the percent variance by subtracting the benchmark number from the new number and then dividing that result by the benchmark number. In this example, the calculation looks like this: (150-120)/120 = 25%. The Percent variance tells you that you sold 25 percent more widgets than yesterday.
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['Ensure your data is in a single range of cells in Excel.', 'If your data represents the entire population, enter the formula "=VAR. ... ', 'The variance for your data will be displayed in the cell.']
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For that, you loop through the data set with a variable, say i and subtract i every time with the mean. Mean can be calculated as mean(dataset) . The result is the variance. So, for calculating the standard deviation, you have to square root the above value.
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['Compute the square of the difference between each value and the sample mean.', 'Add those values up.', 'Divide the sum by n-1. This is called the variance.', 'Take the square root to obtain the Standard Deviation.']
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['Covariance measures the total variation of two random variables from their expected values. ... ', 'Obtain the data.', 'Calculate the mean (average) prices for each asset.', 'For each security, find the difference between each value and mean price.', 'Multiply the results obtained in the previous step.']
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['Step 1: Calculate Actual Cost. Actual Cost = Actual Quantity x Actual Price. ... ', 'Step 2: Find the Standard Cost of Actual Quantity. Standard Cost = Actual Quantity x Standard Price. ... ', 'Step 3: Calculate the Variance.']