b) Determine the mode, median, mean, and standard deviation of the data set: Mod

Question

b) Determine the mode, median, mean, and standard deviation of the data set: Mode = Round your answer to 2 decimal places as needed. Median = Round your answer to 2 decimal places as needed. Mean(Xbar) = Round your answer to 2 decimal places as needed. Standard deviation (S) = Round your answer to 2 decimal places as needed. c) Determine the range of variation: (Xbar - S_1Xbar + S) = (, ) Round your answers to 2 decimal places as needed. Calculate what percent of the data values are within one standard deviation of the mean. Total area of shaded region = Round your answer to 2 decimal places as needed. Percent of area within one standard deviation = % Round your answer to 2 decimal places as needed.

Explanation / Answer

Solution:-

Given the mean and standard deviation of a normal curve, we’d like to approximate the proportion of data that falls within certain intervals.

The Empirical Rule or 68-95-99.7% Rule can give us a good starting point. This rule tells us that around 68% of the data will fall within one standard deviation of the mean; around 95% will fall within two standard deviations of the mean; and 99.7% will fall within three standard deviations of the mean.

Therefore, the total area of shaded region = 0.68

And, Percent of area within one standard deviation = 68%

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