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STANDARD DEVIATION (SD OR ?) While calculating the sample size an investigator needs to anticipate the variation in the measures that are being studied. It is easy to understand why we would require a smaller sample if the population is more homogenous and therefore has a smaller variance or standard deviation.
To calculate the standard deviation of those numbers: Work out the Mean (the simple average of the numbers) Then for each number: subtract the Mean and square the result. Then work out the mean of those squared differences. Take the square root of that and we are done!
Mean and Standard Deviation are most clearly presented in parentheses: The sample as a whole was relatively young (M = 19.22, SD = 3.45). The average age of students was 19.22 years (SD = 3.45).
Standard Deviation First, take the square of the difference between each data point and the sample mean, finding the sum of those values. Next, divide that sum by the sample size minus one, which is the variance. Finally, take the square root of the variance to get the SD.
At the 95% confidence level, the confidence interval is given by ?±1.96?/?n where ? is the mean, ? is the standard deviation and n is the sample size. From the question, we want 1.96?/?n=0.5 and since ?=5, the sample size required is n=(1.96?5/0.5)2=384.16, or 385 after rounding up.