One indicator of an outlier is that an observation is more than 2.5 standard dev

Question

One indicator of an outlier is that an observation is more than 2.5 standard deviations from the mean. Consider the data value 80. (a) If a data set has mean 70 and standard deviation 5, is 80 a suspect outlier? No, since 80 is more than 2.5 standard deviations above the mean. Yes, since 80 is more than 2.5 standard deviations above the mean. No, since 80 is less than 2.5 standard deviations above the mean. Yes, since 80 is less than 2.5 standard deviations above the mean. (b) If a data set has mean 70 and standard deviation 3, is 80 a suspect outlier? No, since 80 is more than 2.5 standard deviations above the mean. Yes, since 80 is more than 2.5 standard deviations above the mean. No, since 80 is less than 2.5 standard deviations above the mean. Yes, since 80 is less than 2.5 standard deviations above the mean.

Explanation / Answer

a)

We have given outlier is 2.5* standard deviation above mean.

If mean 70 and standard deviation is 5 the observation is 70 + 5*2.5 = 82.5.

Since we consider data value is 80, it is less than 82.5(outlier value)

We can't consider 80 as outlier since 80 is less than 2.5 standard deviation above the mean.

b)

mean = 70 and standard deviation is 3

observation would be 70 + 3*2.5 = 77.5

Data value is 80 which is greater than 77.5(outlier value.)

We can consider 80 outlier since 80 is more than 2.5 standard deviation above the mean.

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