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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.
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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.
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.
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.
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.
