find the standard deviation of the first 10 natural numbers.

Question

tell me answer..............

Answer 1

The proper calculation in this case is 

 

                   var =  [ ∑(x_i - mean)² ] / N     (not N-1 because we're not dealing with a sample group)

 

I'm using natural numbers 1,2,3,4,…,10,   some use 0,1,2,…,9 but the result is the same either way:

 

   (1+2+3+4+5+6+7+8+9+10) / 10 = ((10*11)/2) / 10 = 5.5

 

So mean is 5.5

Deltas (each number  - 5.5):

  -4.5, -3.5, -2.5, -1.5, -.5, .5, 1.5, 2.5, 3.5, 4.5

 

Square of deltas:

    20.25, 12.25, 6.25, 2.25, 0.25, 0.25, 2.25, 6.25, 12.25, 20.25

 

Sum of squares of deltas = 82.5

 

                variance =   82.5/10 = 8.25  

                     

          std deviation = √variance  = √8.25 = 2.87

 

 

 

 

Answer 2

The first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.

 

Standard Deviation = 3.02765