If the mean of the following distribution is 6, then value of p is x: 2 4 6 10 p+5 f: 3 2 3 1 2
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If the mean of the following distribution is 6, then value of p is x: 2 4 6 10 p+5 f: 3 2 3 1 2
5
7
6
12
Mean = sum(f*x) / sum(f). Sum(f) = 3+2+3+1+2 = 11. Sum(f*x) = 3(2) + 2(4) + 3(6) + 1(10) + 2(p+5) = 6 + 8 + 18 + 10 + 2p + 10 = 52 + 2p. Mean = (52 + 2p) / 11 = 6. 52 + 2p = 66. 2p = 14, p = 7.
The mean formula gives (3*2 + 2*4 + 3*6 + 1*10 + 2*(p+5)) divided by (3 + 2 + 3 + 1 + 2) = 6. The sum of frequencies is 11, so the numerator must equal 66. Calculating the numerator gives 6 + 8 + 18 + 10 + 2p + 10, which simplifies to 52 + 2p. Setting 52 + 2p = 66 gives 2p = 14, so p = 7.