Explanation
Let A=2 be the arbitrary point. The moments about A are denoted by vr′.
Given:
1. Finding the Mean (xˉ)
The formula to calculate the mean (xˉ) using the first moment about an arbitrary point A is:
xˉ=A+v1′
Substituting the given values:
xˉ=2+1=3
2. Finding the Variance (σ2)
The variance is the second central moment (μ2). The formula to convert moments about an arbitrary point to central moments is:
μ2=v2′−(v1′)2
Substituting the given values:
μ2=16−(1)2
μ2=16−1=15
Conclusion:
The mean of the distribution is 3 and the variance is 15.
Therefore, the correct option is C.
