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A horizontal number line with arrows at both ends is titled at the top as Soccer Team B. Below the line is the title, Number of Goals per Game. The line is numbered 0 to 5 in increments of 1 and has a total of 10 closed points plotted.

there is 2, 2, 3, 3, 3, 3, 3, 3, 4, 4.

Which of the following correctly calculates the average deviation from the mean number of goals per game scored by soccer team B?

(1 point)
Responses

The average deviation from the mean is 0.4.
The average deviation from the mean is 0.4.

The average deviation from the mean is 2.5.
The average deviation from the mean is 2.5.

The average deviation from the mean is 0.2.
The average deviation from the mean is 0.2.

The average deviation from the mean is 0.67.

1 answer

To calculate the average deviation from the mean number of goals per game scored by Soccer Team B, we first need to find the mean.

Here are the steps:

  1. Calculate the mean: The goals scored are: 2, 2, 3, 3, 3, 3, 3, 3, 4, 4.

    • Total goals = 2 + 2 + 3 + 3 + 3 + 3 + 3 + 3 + 4 + 4 = 30
    • Number of games = 10
    • Mean = Total goals / Number of games = 30 / 10 = 3

  2. Calculate the absolute deviations from the mean: Next, we find the absolute deviations of each value from the mean (3):

    • |2 - 3| = 1
    • |2 - 3| = 1
    • |3 - 3| = 0
    • |3 - 3| = 0
    • |3 - 3| = 0
    • |3 - 3| = 0
    • |3 - 3| = 0
    • |3 - 3| = 0
    • |4 - 3| = 1
    • |4 - 3| = 1

    The absolute deviations are: 1, 1, 0, 0, 0, 0, 0, 0, 1, 1.

  3. Calculate the average of the absolute deviations:

    • Total absolute deviations = 1 + 1 + 0 + 0 + 0 + 0 + 0 + 0 + 1 + 1 = 4
    • Average deviation = Total absolute deviations / Number of games = 4 / 10 = 0.4

So, the average deviation from the mean number of goals per game scored by Soccer Team B is 0.4.

Therefore, the correct response is: The average deviation from the mean is 0.4.