As a data analyst with extensive experience in statistical analysis, I understand the importance of standard deviation in understanding the variability of a dataset. It's a crucial measure of dispersion, indicating how spread out the numbers in a dataset are. The standard deviation is the square root of the variance, and it's calculated from the mean of the data set. The variance, in turn, is the average of the squared differences from the mean.

The process of calculating standard deviation typically involves the following steps:

1. Find the Mean: This is the average of all data points.

2. Subtract the Mean: For each data point, subtract the mean to find the deviation.

3. Square the Deviations: Square each of the deviations obtained in the previous step.

4. Average the Squared Deviations: This gives you the variance.

5. Take the Square Root: The square root of the variance gives you the standard deviation.

However, you've asked if it's possible to calculate the standard deviation without first finding the mean. Theoretically, without the mean, you cannot directly calculate the standard deviation because the mean is a prerequisite for finding the variance. The variance is defined as the expected value of the squared difference between the random variable and its mean. Without the mean, you cannot find its variance or standard deviation.

But let's consider a scenario where you might have some information about the dataset but not the mean. If you know only the number of sample points and their sum, you can still calculate the mean, which is the sum of all data points divided by the number of points. Once you have the mean, you can proceed with the steps mentioned above to calculate the standard deviation.

It's important to note that the standard deviation is sensitive to outliers. A few extreme values can significantly affect the standard deviation, making it a less robust measure of spread compared to other measures like the median absolute deviation.

In summary, while it's not possible to calculate the standard deviation without the mean, if you have the sum and count of the data points, you can still find the mean and subsequently calculate the standard deviation. The process requires careful consideration of each step to ensure accuracy.

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The variance is defined as the expected value of the squared difference between the random variable and its mean. Without finding its mean, you cannot find its variance or standard deviation. ... You seem to be asking if you can calculate the sample standard deviation knowing only the number of sample points and their sum.read more >>