1) Find the first four moments about the value 8 for the set of observations: 5,7,8,8,10,11.
2)Find the first four moments about zero for the set of observations : -3,-2,1,3,4.
3) Find the first four moments about mean for the set of observations: 16,19,22,23,25.
4) The first four raw moments of a distribution are 0.9,1.7,3.1 and 8.2 respectively. Find the first four central moments of the distribution.
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Please find below the solution to the asked query:
x | x-0=x | (x-0)2=x2 | (x-0)3=x3 | (x-0)4=x4 |
-3 | -3 | 9 | -27 | 81 |
-2 | -2 | 4 | -8 | 16 |
1 | 1 | 1 | 1 | 1 |
3 | 3 | 9 | 27 | 81 |
4 | 4 | 16 | 64 | 256 |
Total | 3 | 39 | 57 | 435 |
x | x-x̄ | (x-x̄)2 | (x-x̄)3 | (x-x̄)4 |
16 | -5 | 25 | -125 | 625 |
19 | -2 | 4 | -8 | 16 |
22 | 1 | 1 | 1 | 1 |
23 | 2 | 4 | 8 | 16 |
25 | 4 | 16 | 64 | 256 |
Total | 0 | 50 | -60 | 914 |
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