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 shown. 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 Nikita’s mean score before removing the highest and lowest scores compare to her mean score after the highest and lowest scores are removed?
Answer
A
There is not enough information to determine if her score increases or decreases.
B
Her score does not change.
C
Her score is lower after removing the highest and lowest scores.
D
Her score is higher after removing the highest and lowest scores.
Explanation
The full set of eight scores totals 64.5, so the mean before removing scores is 64.5 ÷ 8 = 8.0625. Removing the lowest score, 7.5, and the highest score, 10, leaves a total of 47 across six scores; the new mean is 47 ÷ 6 ≈ 7.83. Since 7.83 is lower than 8.0625, her score is lower after removing the highest and lowest scores.
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