First, calculate the assumed mean 'A' and choose a common factor 'h'. Find the step deviations, \( u_i = (x_i - A)/h \), then compute the mean as \( A + h(\Sigma f_i u_i / \Sigma f_i) \). The standard deviation is \( h \times \sqrt{(\Sigma f_i u_i^2/\Sigma f_i) - (\Sigma f_i u_i/\Sigma f_i)^2} \). I've been using this very method on my father's old calculator to analyse our village's small apple yield surveys, trying to predict if this year's income will be enough. Frankly, these tidy columns feel far removed when the real 'deviation' in our lives depends entirely on the rain.
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