Question

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. nikitas scores on the floor routine from all of the judges are: 7.50, 7.50, 7.75, 7.75, 8.00, 8.00, 8.00, 10.00. how does removing the highest and lowest scores affect the median of the scores? her median score does not change. her median score is lower after removing the highest and lowest scores. her median score is higher after removing the highest and lowest scores. there is not enough information to determine if her median score increases or decreases.

Explanation:

Step1: Arrange scores in ascending order

$7.50, 7.50, 7.75, 7.75, 8.00, 8.00, 8.00, 10.00$

Step2: Calculate median of original scores

There are $n = 8$ scores. The median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+ 1)$-th ordered - values. $\frac{n}{2}=4$ and $\frac{n}{2}+1 = 5$. The median of the original scores is $\frac{7.75 + 8.00}{2}=7.875$.

Step3: Remove highest and lowest scores

The new set of scores after removing $7.50$ and $10.00$ is $7.50, 7.75, 7.75, 8.00, 8.00, 8.00$.

Step4: Calculate median of new scores

There are $n = 6$ scores. The median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+ 1)$-th ordered - values. $\frac{n}{2}=3$ and $\frac{n}{2}+1 = 4$. The median of the new scores is $\frac{7.75 + 8.00}{2}=7.875$.

Answer:

Her median score does not change.