Question

d). if the outliers are removed, which would be more likely to change significantly: the mean or the median? is the standard deviation or interquartile range more likely to change significantly? explain your reasoning.

Explanation:

The mean is calculated as the sum of all values divided by the number of values. Outliers can greatly affect this sum and thus the mean. The median is the middle - value when the data is ordered. Removing outliers doesn't change the position of the middle - value as long as the number of data points doesn't change in a way that affects the middle - value's position. Standard deviation is based on the deviation of each data point from the mean, and inter - quartile range is based on the position of data points (quartiles) and is less affected by outliers.

Answer:

The mean would be more likely to change significantly. The standard deviation would be more likely to change significantly compared to the inter - quartile range. Reason: The mean is sensitive to extreme values (outliers) as it uses all data values in its calculation. The standard deviation measures the spread around the mean, so when outliers are removed, the distances of data points from the mean change, often significantly. The median is the middle value in an ordered data set and is not affected as much by outliers. The inter - quartile range is based on the middle 50% of the data and is less sensitive to extreme values.