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Q: How do you find the sample size when given the standard deviation and the mean with a sample value?

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The sample standard deviation (s) divided by the square root of the number of observations in the sample (n).

A small sample and a large standard deviation

No, the standard deviation is a measure of the entire population. The sample standard deviation is an unbiased estimator of the population. It is different in notation and is written as 's' as opposed to the greek letter sigma. Mathematically the difference is a factor of n/(n-1) in the variance of the sample. As you can see the value is greater than 1 so it will increase the value you get for your sample mean. Essentially, this covers for the fact that you are unlikely to obtain the full population variation when you sample.

The relative standard deviation is the absolute value of the ration of the sample mean to the sample standard deviation. This value appears to be quite small; however, without comparative data it is difficult to know what to make of it. In some contexts it might even be considered large.

Let sigma = standard deviation. Standard error (of the sample mean) = sigma / square root of (n), where n is the sample size. Since you are dividing the standard deviation by a positive number greater than 1, the standard error is always smaller than the standard deviation.

Related questions

Standard deviation in statistics refers to how much deviation there is from the average or mean value. Sample deviation refers to the data that was collected from a smaller pool than the population.

The sample standard deviation (s) divided by the square root of the number of observations in the sample (n).

A small sample and a large standard deviation

No, the standard deviation is a measure of the entire population. The sample standard deviation is an unbiased estimator of the population. It is different in notation and is written as 's' as opposed to the greek letter sigma. Mathematically the difference is a factor of n/(n-1) in the variance of the sample. As you can see the value is greater than 1 so it will increase the value you get for your sample mean. Essentially, this covers for the fact that you are unlikely to obtain the full population variation when you sample.

The relative standard deviation is the absolute value of the ration of the sample mean to the sample standard deviation. This value appears to be quite small; however, without comparative data it is difficult to know what to make of it. In some contexts it might even be considered large.

Let sigma = standard deviation. Standard error (of the sample mean) = sigma / square root of (n), where n is the sample size. Since you are dividing the standard deviation by a positive number greater than 1, the standard error is always smaller than the standard deviation.

It simply means that you have a sample with a smaller variation than the population itself. In the case of random sample, it is possible.

The mean is the average value and the standard deviation is the variation from the mean value.

No. The standard deviation is not exactly a value but rather how far a score deviates from the mean.

No standard deviation can not be bigger than maximum and minimum values.

There is 1) standard deviation, 2) mean deviation and 3) mean absolute deviation. The standard deviation is calculated most of the time. If our objective is to estimate the variance of the overall population from a representative random sample, then it has been shown theoretically that the standard deviation is the best estimate (most efficient). The mean deviation is calculated by first calculating the mean of the data and then calculating the deviation (value - mean) for each value. If we then sum these deviations, we calculate the mean deviation which will always be zero. So this statistic has little value. The individual deviations may however be of interest. See related link. To obtain the means absolute deviation (MAD), we sum the absolute value of the individual deviations. We will obtain a value that is similar to the standard deviation, a measure of dispersal of the data values. The MAD may be transformed to a standard deviation, if the distribution is known. The MAD has been shown to be less efficient in estimating the standard deviation, but a more robust estimator (not as influenced by erroneous data) as the standard deviation. See related link. Most of the time we use the standard deviation to provide the best estimate of the variance of the population.

Z-score is the x value minus the mean, all divided by the standard deviation; or z=(x-mu)/sigma. The "x" value needs to be given to answer the question.

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