Which of the following values is unusual?

Question

The mean of a distribution is 20 and the standard deviation is 5.

30

25

7

11

 

I don't understand how to find the answer.

Answer 1

Not sure what they are asking with the vague word usage of "unusual", but I take that as meaning a statistically significant outlier. 

 

If the mean(average) is 20, then the value of 25 is within 1 std(+ or - 5 from the avg. of 20), 11 and 30 are within 2std (5+5= + or - 10 from avg.), and 7 is within 3 std (+ or - 15 from the avg. of 20).

 

Therefore, the answer they are looking for is 7, as only 5% of the data sample is within this range (5-9.99 and 30.01-35).

 

Think back to that 68-95-99.7 and you will see outside of 2 standard deviations only 5% of the data sampled could exist within this area.

 

If you need some real life examples or a better explanation feel free to reach out.