To determine whether the mean or median is a better measure of the center for the given data set, we first need to calculate both the mean and the median for the number of goals scored in the games.
The goals scored in each game are: 6, 1, 1, 0, 3, 1, 0, 3, 8.
Step 1: Calculate the Mean
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Add all the goals scored: \(6 + 1 + 1 + 0 + 3 + 1 + 0 + 3 + 8 = 23\)
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Divide by the number of games (9): \(\text{Mean} = \frac{23}{9} \approx 2.56\)
Step 2: Calculate the Median
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First, arrange the data in ascending order: \(0, 0, 1, 1, 1, 3, 3, 6, 8\)
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Find the middle value: Since there are 9 numbers (an odd amount), the median is the value in position \( \frac{9 + 1}{2} = 5 \). Thus, the median is \(1\).
Step 3: Analyzing the Data
The dataset has several low values (0s and 1s) and a few high values (6 and 8), which suggests that the data is skewed to the right. In this case, the mean (approximately 2.56) is higher than the median (1), and the presence of high values can affect the mean more than the median.
Conclusion:
Since the data is skewed, the median (1) is a better representative of the center of the data set than the mean (approximately 2.56).
Therefore, the correct response is:
The median value of 1 is the best measure of center that describes the shape of the data set.