Dear researchers, according to the attached image, is there a way to find the standard deviation based on the sample size and mean?
Kind regards
Adel
I am afraid that without knowing either the individual observations or the sum-of-squares (sum of the squared discrepancies around the mean), there is no way of identifying the sample standard deviation. Let me tell you an example. Consider the two datasets (1, 3, 5, 7 and 9) and (3, 4, 5, 6 and 7). Both of them form a sample of n=5 units and possess the same sample mean of 5. Their standard deviation, however, is not the sample. Unfortunately, the sample mean and the sample size are not sufficient to identify the corresponding standard deviation.
You cannot directly calculate the standard deviation from just the mean and the sample size. The standard deviation is a measure of the spread or dispersion of data points around the mean, and it requires the individual data values to be available to compute it accurately.
However, if you have access to the entire dataset, you can use the following steps to calculate the standard deviation from the mean and the dataset:
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