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Usually we only have a sample, the sample variance is the variance of this sample. Given a sample of data of size n , the sample variance is calculated using s2=1n?1n?i=1(xi?¯x)2.
The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.
Steps for calculating the variance by hand Step 1: Find the mean. Step 2: Find each score's deviation from the mean. Step 3: Square each deviation from the mean. Step 4: Find the sum of squares. Step 5: Divide the sum of squares by n ? 1 or N.
Step 1: Find the mean. Step 2: For each data point, find the square of its distance to the mean. Step 3: Sum the values from Step 2. Step 4: Divide by the number of data points.
Both formulas are useful at different times. The first shows the relation to variance of a random variable, which is defined very similiarly (but with n as denominator). The second is useful for actually calculating the sample variance without needing to go calculate the avergae ?x first.