The mean and median must remain the same when the score from James' extra throw is included in the data set.
The mean is the average of all the numbers in the data set. When an additional number is added that is greater than all but one of the other numbers, it will increase the sum of all the numbers in the data set. However, the sum of the numbers will still be divided by the same number of total throws, so the mean will remain the same.
The median is the middle number when the numbers are arranged in order. Since James' extra throw is greater than his previous throws, it will now be the highest number in the data set. Therefore, the new median will be the same as the previous median or the number that was in the middle, which will remain the same.
Mr. Wilson decides to give James an extra throw, and includes the score of the throw to create a new data set. James' score on this throw is greater than his score on all but one of his other throws. Which measure(s) must be the same when the score from James' extra throw is included? Justify your answer.
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