Question

# A data set has a mean of 135, a median of 137, and a standard deviation...

A data set has a mean of 135, a median of 137, and a standard deviation of 13. Marrion concludes that 99.7% of the data in the set must have values between 96 and 174.

What flaw, if any, is there in Marrion’s reasoning? Pick only one.

A. Marrion should have calculated three standard deviations from the median instead of calculating three standard deviations from the mean.

B. There is no flaw in Marrion’s reasoning. He calculated three standard deviations from the mean correctly to find the values 96 and 174. Then he used the 68−95−99.7 rule to determine that approximately 99.7% of the data is in that range.

C. Marrion should have calculated at least three standard deviations from the mean instead of only two standard deviations from the mean.

D. The data does not appear to be normally distributed, so Marrion can’t use the 68−95−99.7 rule. When a median is so different from the mean, it’s likely that the data is not normally distributed.

given that mean = 135, median= 137 and standard deviation = 13

using empirical rule, we know that 99.7% of data values fall within 3 standard deviation from the mean

this gives us

mean - 3*sd = 135 - 3*13 = 135 - 39 = 96

and

mean + 3*sd = 135 + 3*13 = 135 + 39 = 174

So, it is clear that the calculation done by Marrion is correct

therefore, only opion B is correct

option A is incorrect because we never calculate the data using median

option C is incorrect because 96 and 174 are not 2 standard deviations from the mean

option D is incorrect because we can assume that the data is normally distributed