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?

Answer 1

Answer:

26

Step-by-step explanation:

The mean of a set of number is the average the set of number, it is the ratio of the total sum of the terms to the sum of terms.

The standard deviation is the variation of a set of numbers to their mean. A low standard deviation means the value are close to the mean and a high standard deviation means the values are far from the mean. The standard deviation is given as:

$\sigma=\sqrt{\frac{\Sigma (x_i-\mu)^2}{n} }\\ \\\mu=mean,n=number\ of\ terms, \sigma=standard\ deviation$

Given the numbers:

86, 81, 87, 82. mean = μ = 84

$\Sigma(x_i-\mu)^2=(86-84)^2+(81-84)^2+(87-84)^2+(82-84)^2=4+9+9+4=26$

Sum of squared deviations = 26

Answer 2

The sum of the squared deviations of the scores from the mean is 26.

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• The observations are: 86, 81, 87 and 82.
• The mean of the observations is 84.
• The sum of the squared deviations of the scores from the mean is the sum of the differences squared of each observation and the mean.

Thus:

$S_{ds} = (86-84)^2 + (81-84)^2 + (87-84)^2 + (82-84)^2 = 4 + 9 + 9 + 4 = 26$

The sum of the squared deviations of the scores from the mean is 26.

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