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Sum of values of x

Sample mean equals the sum of the values of x divided by the number of values n.

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Formula for standard deviation

The formula for standard deviation, or the square root of the difference between the random value and the expected value squared times the probability of the random variable.

Formula (equivalent) for standard deviation

An alternative formula for standard deviation, or the square root of the difference between the mean (average) of the squared observed values and the mean of the observed values squared.

Square root of the squares

The square root of the squares of the difference between each observation and the expected value multiplied by their probabilities. The first term inside the square root is the first value, 0, minus the expected value or mean, 1.9, all squared, and multiplied by the probability of a 0, or 0.1, and so on for the next value, summed for all values and then take the root.

The square root of 0.89

The square root of 0.89.

Square root of the difference between the squares

The square root of the difference between the squares of the values times their probability, 4.5, and the square of the expected value or 1.9 squared.

The standard error

The standard error (standard deviation of the sample mean) is equal to the standard deviation of the population mean of x divided by the square root of the number of observations n.

The standard error of the sample mean

The standard deviation of the population mean of x divided by the square root of the number of observations n.

Standard error is estimated

The standard error of the sample is equal to the standard deviation of the sample divided by the square root of the number of observations n, which in this case is 13.63 divided by the square root of 20, or 3.05.

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