The standard deviation measures the standard (or typical) distance from the mean

Question

The standard deviation measures the standard (or typical) distance from the mean. For each of the following two populations, you should be able to use this definition to determine the standard deviation without doing any serious calculations. Sample 1: 2, 4, 2, 4 Sample 2: 7, 7, 7, 7 Can a SS (sums of squares) ever have a value less than zero? Explain your answer In general, what does it mean for a sample to have a standard deviation of zero? Describe the scores in such a sample. Sketch a normal distribution with a mean of 50. Then drop a vertical one standard deviation (SD 20) above the mean and a second one 1 standard deviation (SD) below the mean. Use figure 4.6 as your guide. I labeled the X axis for you. What score falls 1 SD above the mean?

Explanation / Answer

3.

Lets find mean of samples first = 2+4+2+4 / 4 = 3

Mean of sample 2 = 7+7+7+7/4 = 7

Deviation of 2nd sample is 0

Lets find deviation in 2nd sample = sqrt( (2-3)^2 +(4-3)^2 +(2-3)^2 +(4-3)^2 / 4) = sqrt( 1+1+1+1/4) = 1

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