The table shows the distances that schools will travel to attend a field trip to the state capitol. School 7 has to travel 15 miles. If this outlier is added to the data, which is a true statement about how it changes the data in the table?

Question

Select all statements that apply.

Answer 1

To provide a clear response regarding the effect of adding an outlier (like School 7's 15 miles) to a dataset, we would need to consider statistical properties. However, since I cannot see the table you mentioned, I can explain generally how an outlier can affect data:

1. Mean: The mean (average) of the dataset will likely increase if the value of the outlier is greater than the existing mean. If the existing distances were significantly lower, the inclusion of 15 miles would pull the average up.

2. Median: The median (the middle value of the dataset when ordered) may change depending on the position of the outlier in the ordered list. If the outlier is higher than the median, and if the number of data points is even, the median could potentially increase.

3. Range: The range (the difference between the maximum and minimum values) will increase if the outlier is a higher value than the maximum distance previously in the data.

4. Standard Deviation/Variance: The standard deviation is likely to increase due to the presence of the outlier, as it increases the overall variability in the data set.

Overall, including an outlier tends to distort overall characteristics of a dataset, especially those that are sensitive to extreme values like the mean and standard deviation. If you provide specific statements about the impact of the outlier, I can help you evaluate which ones are true.