b. (i) For \( n=2 \), the mean is 3.50 and the standard deviation is (Round to two decimal places as needed.)
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The Deep Dive
To find the standard deviation for \( n = 2 \) with a mean of 3.50, you would typically need the individual data points. However, if you have the variance, standard deviation can be found by taking the square root of the variance. Assuming you're calculating from a dataset, remember this: the standard deviation formula is: \(\sigma = \sqrt{\frac{\sum (x - \mu)^2}{n}}\). On rounding, make sure all calculations maintain precision until the final step to ensure accuracy in your rounded results! To avoid common mistakes when calculating the standard deviation, ensure you properly account for the number of data points when finding the mean and the variance. Remember that with a small sample size, each data point has a significant impact on the final result. Additionally, don’t forget to square your deviations; many tend to skip this step! Using a calculator or software can also help mitigate human error in complex calculations.
