HELP!! std. dev, mode and mean.

Question

There are 5 participants in a study. All I have are some statistics to find out the individual numbers for the 5 people. The mean is 8, the standard deviation is 4, the mode is 5 and the range is 12. Can you figure out what the 5 numbers are? An explaination would also be great!

Answer 1

Let's do some trial and error and see what we can learn.

 

If there are 5 scores and the mean is 8 then (? + ? + ? + ? + ?)/5 =8.

Multiple both sides of the equation by 5 and we get (? + ? + ? + ? + ?) = 40, that is, the sum of the scores is 40.

 

The set [8,8,8,8,8] has a mean of 8 but the standard deviation = 0, mode = 8, and range is 0; all wrong.

 

The set [6,7,8,9,10] has the correct mean but mode is undefined, and range = 4.

 

Can we find a set that has the correct mean and mode?

 

Yes. The set [1,5,5,14,15] has the desired mean and mode. The range is 15-1=14; too big;

 

The set [3,5,5,13,14] has the desired mean and mode. The range is 14-3=11; too small;

 

The set [3,5,5,12,15] works for mean, mode and range, but what about standard deviation?

The sum of the residuals squared is (3-8)^2 + (5-8)^2 + (5-8)^2 +(12-8)^2 + (15-8)^2

= 25 + 9 + 9 + 16 + 49 = 108

 

std dev = sqrt(108/5) = 4.65 (So close!)

 

Notice that we can't change either of the 5's in this set because that would change the mode.

 

Can you solve it from here?