The standard deviation (SD) is a measure of how spread out a set of data points are from their mean value. In other words, it tells us how far apart each data point is from the average value of that set of data. The SD is calculated by taking the square root of the variance, which measures the average of the squared differences between each data point and the mean.

However, when we have a constant value, the standard deviation becomes zero. This is because a constant value is an exact number and has no variation or spread. Therefore, it is impossible for a constant value to have a non-zero SD.

It’s important to note that while a constant value may seem like a straightforward answer, in reality, it can be a bit more complex. For example, if you have a dataset that includes both constant values and variable values, the constant values will have an SD of zero, but the variable values will not. Additionally, if your dataset is a sample from a larger population, there may still be some variation within the sample, even if it’s just random error.

In summary, the standard deviation of a constant value is always zero. It is important to understand this concept in order to correctly interpret and analyze data that includes both constant and variable values.