Which of the following values is unusual?

Question

The mean of a distribution is 100 and the standard deviation is 10.

 

130

80

120

90

Answer 1

Following the pattern I tried to describe in your previous question, start with your mean of 100 & mark 3 increments of 10 both below & above 100. The most common cases will fall right around 100 - from 90 to 110. The 2nd SD will include 80-89 & 111-120. The 3rd SD (called outliers) will cover 70-79 & 121-130. I trust you can see that 130 is an extreme case in this distribution & lies as far out as is possible under the given conditions. The definition of the "normal distribution" precludes any results beyond -/+3 standard deviations - in this case -3SD X 10 (-30) & +3SD X 10 (+30). All the data exists therefore in the range of 100-30 to 100+30 - or 70 to 130.