First slide

Introduction to statistics

Question

$If \sum_{i = 1}^{18} (x_{i} - 8) = 9 and \sum_{i = 1}^{18} {(x_{i} - 8)}^{2} = 45 then the standard deviation of x_{1}, x_{2} \dots x_{18} is$

Moderate

Solution

$Let d_{i} = x_{i} - 8 but σ_{x}^{2} = σ_{d}^{2} = \frac{1}{18} Σ d_{i}^{2} - {(\frac{1}{18} Σ d i)}^{2} = \frac{1}{18} \times 45 - {(\frac{9}{18})}^{2} = \frac{5}{2} - \frac{1}{4} = \frac{9}{4} .$
$∴ σ_{x} = \frac{3}{2}$

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