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 the formula for sum of squared deviations

The sum of squared deviations of data - points $x_i$ from the mean $\bar{x}$ is given by $\sum_{i}(x_i - \bar{x})^2$. Here, $x_1 = 86$, $x_2 = 81$, $x_3 = 87$, $x_4 = 82$ and $\bar{x}=84$.

Step2: Identify the correct expression

Substituting the values into the formula, we get $\sum(x - \bar{x})^2=(86 - 84)^2+(81 - 84)^2+(87 - 84)^2+(82 - 84)^2$.

Answer:

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