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Q: Can a standard deviation of a sample be equal to a standard deviation of a population?

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Sure it can. But in the survey business, the trick is to select your sample carefully so that they'll be equal, i.e. a sample that is accurately representative of the population.

Standard deviation can only be zero if all the data points in your set are equal. If all data points are equal, there is no deviation. For example, if all the participants in a survey coincidentally were all 30 years old, then the value of age would be 30 with no deviation. Thus, there would also be no standard deviation.A data set of one point (small sample) will always have a standard deviation of zero, because the one value doesn't deviate from itself at all.!

no the standard deviation is not equal to mean of absolute distance from the mean

A standard deviation of zero means that all the data points are the same value.

The mean and variance are equal in the Poisson distribution. The mean and std deviation would be equal only for the case of mean = 1. See related link.

Related questions

Sure it can. But in the survey business, the trick is to select your sample carefully so that they'll be equal, i.e. a sample that is accurately representative of the population.

98.73

True.

If I take 10 items (a small sample) from a population and calculate the standard deviation, then I take 100 items (larger sample), and calculate the standard deviation, how will my statistics change? The smaller sample could have a higher, lower or about equal the standard deviation of the larger sample. It's also possible that the smaller sample could be, by chance, closer to the standard deviation of the population. However, A properly taken larger sample will, in general, be a more reliable estimate of the standard deviation of the population than a smaller one. There are mathematical equations to show this, that in the long run, larger samples provide better estimates. This is generally but not always true. If your population is changing as you are collecting data, then a very large sample may not be representative as it takes time to collect.

yes

You calculate the standard error using the data.

Standard deviation can only be zero if all the data points in your set are equal. If all data points are equal, there is no deviation. For example, if all the participants in a survey coincidentally were all 30 years old, then the value of age would be 30 with no deviation. Thus, there would also be no standard deviation.A data set of one point (small sample) will always have a standard deviation of zero, because the one value doesn't deviate from itself at all.!

The standard deviation must be greater than or equal to zero.

If n = 1.

The variance

no the standard deviation is not equal to mean of absolute distance from the mean

Yes.