The mean of six numbers is calculated. The deviations of the numbers from the mean are -4.5. 3, 2. d, 1. Detemine the value of d and hence find the exact variance of the numbers.

Question

The mean of six numbers is calculated. The deviations of the numbers from the mean are
-4.5. 3, 2. d, 1.
Determine the value of d and hence find the exact variance of the numbers.

Answer 1

0= ∑ fd
          f
−3 + d = 0
     6
d = 3
Variance= ∑ ƒd²
                   ∑ ƒ
= 16+25+9+4+1+d²
           6
= 55+3²
       6
=  10 ²/₃