The values of a set of data are 3, 4, 6, 2, 4, 2, 3, 1, 5, 3, 4, 3, 5. What is the range of values within two standard deviations of the mean?

Question

The values of a set of data are 3, 4, 6, 2, 4, 2, 3, 1, 5, 3, 4, 3, 5. What is the range of values within two standard deviations of the mean?

Answer 1

Hi Eryn,

Usually your calculator can to this for you if you have a "STAT" option.

 

"the range of values within 2 standard deviations of the mean" is the numbers that fall between (mean + 2 sds) and the (mean - 2 sds).  So you first must calculate the mean.  I went to an online standard deviation calculator and gave it your data points.  It tells me that the mean is 3.46154 and that the standard deviation (sd) is 1.33678

 

So we must calculate (mean - 2 sds) = 3.46154 - 2 * 1.33678  = 0.78798    This is the low end of the range they want.

 

Then calculate (mean + 2 sds) = 3.46154 + 2 * 133678 = 6.1351   The is the upper end of the range they want.

 

So the smallest data value that fits in the range 0.78798 to 6.1351 is 1  and the largest data value that fits within this range is 6.   

 

When asked for the "range" of values, by definition this is the largest data value minus the smallest data value, so I think your answer would be 6 - 1 = 5.  If the teacher wants a list of the data points that fall within 2 sds of the mean, then I would answer with the set  {1,2,3,4,5,6}.  The range of this set is 6 - 1 = 5.