Question

a golfer recorded the following scores for each of four rounds of golf: 86, 81, 87, 82. the mean of the scores is 84. what is the sum of the squared deviations of the scores from the mean? (a) $sum(x - \bar{x})=(86 - 84)+(81 - 84)+(87 - 84)+(82 - 84)$ (b) $sum|x - \bar{x}|=|86 - 84|+|81 - 84|+|87 - 84|+|82 - 84|$ (c) $2sum|x - \bar{x}|=2|86 - 84|+|81 - 84|+|87 - 84|+|82 - 84|$ (d) $sum(x - \bar{x})^2=(86 - 84)^2+(81 - 84)^2+(87 - 84)^2+(82 - 84)^2$ (e) $sum|x - \bar{x}|^2=|86 - 84|+|81 - 84|+|87 - 84|+|82 - 84|^2$

Explanation:

Step1: Recall formula for squared - deviation sum

The sum of squared deviations of scores \(x\) from the mean \(\bar{x}\) is given by \(\sum(x - \bar{x})^2\).

Step2: Identify correct option

Given scores and mean, the correct expression is \(\sum(x - \bar{x})^2=(86 - 84)^2+(81 - 84)^2+(87 - 84)^2+(82 - 84)^2\), which is option D.

Answer:

D. \(\sum(x - \bar{x})^2=(86 - 84)^2+(81 - 84)^2+(87 - 84)^2+(82 - 84)^2\)