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 shown below. 7.50, 7.50, 7.75, 7.75, 8.00, 8.00, 8.00, 10.00 how does nikitas mean score before removing the highest and lowest scores compare to her mean score after the highest and lowest scores are removed? her score does not change. her score is lower after removing the highest and lowest scores. her score is higher after removing the highest and lowest scores. there is not enough information to determine if her score increases or decreases.

Explanation:

Step1: Calculate the mean before removing scores

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 8$, and the scores are $x=\{7.50,7.50,7.75,7.75,8.00,8.00,8.00,10.00\}$. So, $\sum_{i=1}^{8}x_{i}=7.50\times2 + 7.75\times2+8.00\times3 + 10.00=15 + 15.5+24 + 10=64.5$. The mean $\bar{x}_1=\frac{64.5}{8}=8.0625$.

Step2: Remove the highest and lowest scores

The lowest score is $7.50$ and the highest score is $10.00$. After removing them, $n = 6$, and the scores are $x=\{7.50,7.75,7.75,8.00,8.00,8.00\}$. $\sum_{i = 1}^{6}x_{i}=7.50+7.75\times2+8.00\times3=7.50 + 15.5+24=47$. The mean $\bar{x}_2=\frac{47}{6}\approx7.83$.

Step3: Compare the means

Since $8.0625>7.83$, her score is lower after removing the highest and lowest scores.

Answer:

Her score is lower after removing the highest and lowest scores.