The eight measurements (in cm) of the diameter of small discs cut from a sheet of…

MATHEMATICS · Subjective · A Level · Mathematics · Data presentation and interpretation · Data presentation and interpretation

Problem

The eight measurements (in cm) of the diameter of small discs cut from a sheet of metal are: 3, 5, 7, 9, 11, 13, 15, 17. Answer the following: (i) Compute ∑xi\displaystyle \sum x_i and ∑xi2\displaystyle \sum x_i^2 for the above data. (ii) Starting only from the definition σ2=1n∑(xi−xˉ)2\displaystyle \sigma^2 = \frac{1}{n}\sum (x_i-\bar{x})^2, derive an expression for σ2\sigma^2 that involves ∑xi\sum x_i and ∑xi2\sum x_i^2 but does not contain any term of the form (xi−xˉ)(x_i-\bar{x}). (iii) Using the result of part (ii), calculate the variance and standard deviation of the given data set, showing every algebraic step clearly.

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