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Why take the square root of the variance when calculation standard deviation?
The variance is based on the squares of the variable being studied. If, for example, the variable is mass, then the variance is measured in mass-squared. Most people will not be able to wrap their heads around the square of mass. However, the square root will be in the same units of measurement as the variable itself. Thus, the idea of a variable being distributed about a mean, M (also measured in the same units), with a standard deviation (or error) of S is easier to understand.Second, under reasonable conditions,the transformed variable obtained by subtracting the mean and dividing the result by the standard deviation will have a standard normal distribution. This is extremely important for estimation and hypothesis testing.
What is a difference between a pooled variance and a combined variance?
Pooled variance is a method for estimating variance given several different samples taken in different circumstances where the mean may vary between samples but the true variance (equivalently, precision) is assumed to remain the same. A combined variance is a method for estimating variance from several samples, given the size, mean and standard deviation of each. Mathematically, a combined variance is equal to the calculated variance of the set of the data from all samples. See links.
How do you calculate mean average deviation?
The mean average deviation is the same as the mean deviation (or the average deviation) and they are, by definition, 0.
Is the standard deviation the same as the mean of absolute distances from the mean?
no the standard deviation is not equal to mean of absolute distance from the mean
What does homogeneity of variance mean?
It means that the variance remains the same across the range of values of the variable.
Is the variance of a group of scores the same as the squared standard deviation?
The standard deviation is defined as the square root of the variance, so the variance is the same as the squared standard deviation.
What is the relationship between standard deviation and variance for the same sample data?
The standard deviation is the square root of the variance.
Does variance provide more information than standard deviation?
No. Because standard deviation is simply the square root of the variance, their information content is exactly the same.
What is the relationship between the mean and standard deviation in statistics?
The 'standard deviation' in statistics or probability is a measure of how spread out the numbers are. It mathematical terms, it is the square root of the mean of the squared deviations of all the numbers in the data set from the mean of that set. It is approximately equal to the average deviation from the mean. If you have a set of values with low standard deviation, it means that in general, most of the values are close to the mean. A high standard deviation means that the values in general, differ a lot from the mean. The variance is the standard deviation squared. That is to say, the standard deviation is the square root of the variance. To calculate the variance, we simply take each number in the set and subtract it from the mean. Next square that value and do the same for each number in the set. Lastly, take the mean of all the squares. The mean of the squared deviation from the mean is the variance. The square root of the variance is the standard deviation. If you take the following data series for example, the mean for all of them is '3'. 3, 3, 3, 3, 3, 3 all the values are 3, they're the same as the mean. The standard deviation is zero. This is because the difference from the mean is zero in each case, and after squaring and then taking the mean, the variance is zero. Last, the square root of zero is zero so the standard deviation is zero. Of note is that since you are squaring the deviations from the mean, the variance and hence the standard deviation can never be negative. 1, 3, 3, 3, 3, 5 - most of the values are the same as the mean. This has a low standard deviation. In this case, the standard deviation is very small since most of the difference from the mean are small. 1, 1, 1, 5, 5, 5 - all the values are two higher or two lower than the mean. This series has the highest standard deviation.
How do you calculate salary variance?
I believe you are interested in calculating the variance from a set of data related to salaries. Variance = square of the standard deviation, where: s= square root[sum (xi- mean)2/(n-1)] where mean of the set is the sum of all data divided by the number in the sample. X of i is a single data point (single salary). If instead of a sample of data, you have the entire population of size N, substitute N for n-1 in the above equation. You may find more information on the interpretation of variance, by searching wikipedia under variance and standard deviation. I note that an advantage of using the standard deviation rather than variance, is because the standard deviation will be in the same units as the mean.
Can the variance be zero?
Variance is standard deviation squared. If standard deviation can be zero then the variance can obviously be zero because zero squared is still zero. The standard deviation is equal to the sum of the squares of each data point in your data set minus the mean, all that over n. The idea is that if all of your data points are the same then the mean will be the same as every data point. If the mean is the equal to every data point then the square of each point minus the mean would be zero. All of the squared values added up would still be zero. And zero divided by n is still zero. In this case the standard deviation would be zero. Short story short: if all of the points in a data set are equal than the variance will be zero. Yes the variance can be zero.
Why take the square root of the variance when calculation standard deviation?
The variance is based on the squares of the variable being studied. If, for example, the variable is mass, then the variance is measured in mass-squared. Most people will not be able to wrap their heads around the square of mass. However, the square root will be in the same units of measurement as the variable itself. Thus, the idea of a variable being distributed about a mean, M (also measured in the same units), with a standard deviation (or error) of S is easier to understand.Second, under reasonable conditions,the transformed variable obtained by subtracting the mean and dividing the result by the standard deviation will have a standard normal distribution. This is extremely important for estimation and hypothesis testing.
What is the difference between standard error of mean and standard deviation of means?
Standard error of the mean (SEM) and standard deviation of the mean is the same thing. However, standard deviation is not the same as the SEM. To obtain SEM from the standard deviation, divide the standard deviation by the square root of the sample size.
Variance and standard deviation are one and the same thing?
No. But they are related. If a sample of size n is taken, a standard deviation can be calculated. This is usually denoted as "s" however some textbooks will use the symbol, sigma. The standard deviation of a sample is usually used to estimate the standard deviation of the population. In this case, we use n-1 in the denomimator of the equation. The variance of the sample is the square of the sample's standard deviation. In many textbooks it is denoted as s2. In denoting the standard deviation and variance of populations, the symbols sigma and sigma2 should be used. One last note. We use standard deviations in describing uncertainty as it's easier to understand. If our measurements are in days, then the standard deviation will also be in days. The variance will be in units of days2.
What words mean the same as difference?
Dissimilarity, distinctness, disparity, exception, contrast, deviation, peculiarity, variance, argument, clash, conflict, dissent, discord, strife...
Which type of measure of dispersion is mostly used standard deviation or variance?
They are effectively the same but the standard deviation is more popular because the units of measurement are the same as those for the variable.
Why is the standard deviation used more frequently than the variance?
The standard deviation has the same measurement units as the variable and is, therefore, more easily comprehended.
