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.

Answer 1

Answer:

a) No, since 80 is less than 2.5 standard deviations above the mean; b) Yes, since 80 is more than 2.5 standard deviations above the mean.

Step-by-step explanation:

For part a,

The mean is 70 and the standard deviation is 5.  This means that 2 standard deviations above the mean is 70+5+5 = 80.

This means that 80 is not an outlier, as it is not more than 2.5 standard deviations above the mean.

For part b,

The mean is 70 and the standard deviation is 3.  This means that 2 standard deviations above the mean is 70+3+3 = 76; 3 standard deviations above the mean is 70+3+3+3 = 79.  80 is more than this, so yes, it is an outlier.