In some gymnastics meets, the score given to a gymnast is the mean of the judges’ scores after the highest and lowest scores have been tossed out. Nikita’s scores on the floor routine from all of the judges are: 7 point 5 0 , 7 point 5 0 , 7 point 7 5 , 7 point 7 5 , 8 point 0 0 , 8 point 0 0 , 8 point 0 0 , 10 point 0 0 How does removing the highest and lowest scores affect the median of the scores?
Answer
A
Her median score does not change.
B
There is not enough information to determine if her median score increases or decreases.
C
Her median score is higher after removing the highest and lowest scores.
D
Her median score is lower after removing the highest and lowest scores.
Explanation
The original scores in order have a median equal to the average of the 4th and 5th scores: (7.75 + 8.00) ÷ 2 = 7.875. After removing the lowest score, 7.50, and the highest score, 10.00, the middle two of the remaining six scores are 7.75 and 8.00. Their average is also 7.875, so her median does not change.
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