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No. Well not exactly.
The square of the standard deviation of a sample, when squared (s2) is an unbiased estimate of the variance of the population.
I would not call it crude, but just an estimate. An estimate is an approximate value of the parameter of the population you would like to know (estimand) which in this case is the variance.
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What does the standard deviation tell us?
standard deviation is the square roots of variance, a measure of spread or variability of data . it is given by (variance)^1/2
What is used as a measure of total risk?
The standard deviation or volatility (square root of the variance) of returns.
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 a Measure of spread about the mean?
Standard error, standard deviation, variance, range, inter-quartile range as well as measures based on other percentiles.
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.
