Consider a set of observations ${x_1}, {x_2}, {x_3}, ..., {x_{101}}$ such that ${x_1} < {x_2} < {x_3} < ... < {x_{100}} < {x_{101}}$. The mean deviation of this set of observations about a point $k$ is minimum when $k$ equals:
- A${x_1}$
- B${x_{51}}$
- C$\frac{{x_1} + {x_2} + ... + {x_{101}}}{101}$
- D${x_{50}}$
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Find the weighted mean of the first $n$ natural numbers,where the weights are equal to their squares.
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