Standard deviation and examples

1.  If a mean of a dataset is 25 and the standard deviation is 1.6, what can be said about the data within 1, 2 and 3 standard deviations? Assuming a normal distribution.

Answer:

i.    68% of all values lie between 25 – 1.6 and 25 + 1.6.

      That’s 68% of data values lie between 23.4 and 26.6.

ii.   95% of all values lie between 25 – (1.6 x 2) and 25 + (1.6 x 2)

      That’s 95% of data values lie between 21.8 and 28.2

 And finally

iii.  99.7% of all the values lie between 25 – (1.6 x 3) and 25 + (1.6 x 3)

     That’s 99.7% of data values lie between 20.2 and 29.8.

2.  The teacher announces that the average score on the latest test was 80/100 with a standard deviation of 5. What did 68% of the class get in their results?

Answer:

1 SD = 68%

So 68% of the class were 1 SD away from the mean.

Which means that:

68% of the class received a score between  75/100 and 85/100.