Question
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b. (i) For \( n=2 \), the mean is 3.50 and the standard deviation is (Round to two decimal places as needed.)

Ask by Gough Evans. in the United States
Mar 20,2025

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Answer

Cannot determine the standard deviation with the given information.

Solution

To find the standard deviation for \( n=2 \) with a mean of 3.50, we need to know the individual data points or the variance. However, since the problem does not provide specific data points or variance, we cannot calculate the standard deviation directly. If you have the data points or the variance, please provide them, and I can help you calculate the standard deviation. If you need a general formula for standard deviation, it is given by: \[ \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{n}} \] where: - \( \sigma \) is the standard deviation, - \( x_i \) are the data points, - \( \mu \) is the mean, - \( n \) is the number of data points. Please provide additional information to proceed.

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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.

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