Question

mariela earned the following test scores in math: 95, 90, 100, 85, 80. mr. adams accidentally entered marielas next test score as 0. which of these statements are true? check all that apply. before the error, the mean and the median were both 90. before the error, the mean was 90 and the median was 100. the error added an outlier to the data set. after the error, the median remained the same. after the error, the mean was 75 and the median was 87.5. the mean was impacted by the error more than the median. only the median was impacted by the error.

Explanation:

Step1: Calculate original mean

The original data set is \(95,90,100,85,80\). The sum is \(95 + 90+100 + 85+80=450\). The number of data - points \(n = 5\). The original mean \(\bar{x}_1=\frac{450}{5}=90\).

Step2: Calculate original median

Arrange the original data set in ascending order: \(80,85,90,95,100\). The median \(M_1 = 90\) (since \(n = 5\), the middle - value is the third one).

Step3: Calculate new mean after adding outlier

The new data set is \(80,85,90,95,100,0\). The sum is \(80 + 85+90+95+100 + 0=450\). The number of data - points \(n = 6\). The new mean \(\bar{x}_2=\frac{450}{6}=75\).

Step4: Calculate new median after adding outlier

Arrange the new data set in ascending order: \(0,80,85,90,95,100\). The median \(M_2=\frac{85 + 90}{2}=87.5\) (since \(n = 6\), the median is the average of the third and fourth values).

Step5: Analyze the impact

The mean changed from \(90\) to \(75\) (a change of \(90 - 75 = 15\)), and the median changed from \(90\) to \(87.5\) (a change of \(90 - 87.5 = 2.5\)). The mean was impacted more than the median.

Answer:

The mean was impacted by the error more than the median. After the error, the mean was 75 and the median was 87.5.