Question

1. What is the key difference between a population standard deviation and the standard deviation of a sampling distribution?

2. How does this effect the normal distribution for the sample? (i.e. shape)

Answer 1

Standard deviation measures the spread of data distribution. It measures the typical distance between each data point and the mean.
The formula we use for standard deviation depends on whether the data is being considered a population of its own, or the data is a sample representing a larger population.
If the data is being considered a population on its own, we divide by the number of data points, NNN.
If the data is a sample from a larger population, we divide by one fewer than the number of data points in the sample, n-1.

Population standard deviation:

     
   sigma, equals, the square root of, start fraction, sum, left parenthesis, x, start subscript, i, end subscript, minus, mu, right parenthesis, start superscript, 2, end superscript, divided by, N, end fraction, end square root
Sample standard deviation:

     
The steps in each formula are all the same except for one—we divide by one less than the number of data points when dealing with sample data.