Question

which of the following correctly calculates the average deviation from the mean number of goals per game scored by soccer team b? (1 point) the average deviation from the mean is 0.2. the average deviation from the mean is 0.67. the average deviation from the mean is 0.4. the average deviation from the mean is 2.5.

Explanation:

Step1: Calculate the mean

Assume the data points (goals per game) are \(x_1,x_2,x_3\). Let's say the data is \(2,3,4\) (from the graph - assuming 3 data points as per the vertical marks with dots). The mean \(\bar{x}=\frac{2 + 3+4}{3}=\frac{9}{3}=3\).

Step2: Calculate the absolute deviations

The absolute deviations are \(|x_1-\bar{x}|,|x_2 - \bar{x}|,|x_3-\bar{x}|\).
For \(x_1 = 2\): \(|2 - 3|=1\)
For \(x_2=3\): \(|3 - 3|=0\)
For \(x_3 = 4\): \(|4 - 3|=1\)

Step3: Calculate the average deviation

The average deviation (mean absolute deviation) \(=\frac{1+0 + 1}{3}=\frac{2}{3}\approx0.67\)

Answer:

The average deviation from the mean is \(0.67\)