Question

The weighted GM of the four number 8,25,17 and 30 is 15.3 If the weights of the first three numbers are 5,3 and 4 respectively,find the weight of the fourth number​

Answer 1

15.3=a.l[(0.698+0.477+0.602+log(c))\4]

Answer 2

Answer:

weight of fourth observation = 2

Step-by-step explanation:

given, the numbers are 8, 25, 17, 30

their geometric mean = 15.3

the weight given for the first 3 numbers is 5, 3, 4

let x be the weight of the fourth number

GM = antilog[∑w.㏒x/ ∑w]

x     weight      ㏒x          w.㏒x

8        5           0.9031      4.1555

25      3           1.3979       4.1938

17       4            1.2304      4.9218

30      x            1.4771        1.4771x

         12+x                       13.6311+1.4771x

㏒ GM = ∑w.㏒x/ ∑w

㏒  15.3 = $\frac{13.6311+1.4771x}{12+x}$

1.1847 = $\frac{13.6311+1.4771x}{12+x}$

14.2163 + 1.1847x = 13.6311 + 1.4771x

⇒0.5852 = 0.2924x

⇒x = $\frac{0.5852}{0.2924}$ = 2

therefore, weight of fourth observation = 2