Use the table to answer the question.
Game Runs Scored
1 0
2 7
3 2
4 9
5 1
6 1
7 10
What value, the mean or the median, best describes the shape of the data set that contains the number of runs scored by the baseball team? Choose 1 for mean and 2 for median.
(1 point)
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To determine whether the mean or the median best describes the shape of the data set, we need to examine the values in the data set. The mean is calculated by adding up all the values and then dividing by the total number of values. The median is the middle value when the data set is arranged in order.
In this case, the data set is as follows:
0, 7, 2, 9, 1, 1, 10
The mean is calculated by adding up all the values and then dividing by 7. The sum of the values is 30, so the mean is 30/7, which is approximately 4.29.
To find the median, we arrange the values in order:
0, 1, 1, 2, 7, 9, 10.
Since there are 7 values, the median is the middle value, which in this case is 2.
Comparing the mean of 4.29 to the median of 2, we can see that the median is a better descriptor of the shape of the data set because it represents the middle value and is not influenced by outliers like the mean can be. Therefore, the answer is 2 for median.
To determine whether the mean or the median best describes the shape of the data set, we need to consider the distribution of the data.
To calculate the mean, we add up all the values and divide by the total number of values. In this case, adding up all the runs scored gives us a total of 30 runs. Since there are 7 games, the mean number of runs scored would be 30 divided by 7, which is approximately 4.29.
The median, on the other hand, is the middle value when all the values are arranged in ascending or descending order. In this case, the runs scored are already listed in order: 0, 1, 1, 2, 7, 9, 10. The middle value is 2.
Comparing the mean of approximately 4.29 to the median of 2, we can see that the mean is greater. This suggests that the data is skewed to the right, or positively skewed.
Therefore, the value that best describes the shape of the data set is the mean (1).