Question

roger claims that the two statistics most likely to change greatly when an outlier is added to a small data set are the mean and the median. is rogers claim correct? a yes, both the mean and median are likely to change greatly b no, only the mean is likely to change greatly. c no, only the median is likely to change greatly. d no, neither the mean nor the median are likely to change greatly. e there is not enough information to determine if the mean or the median is likely to change greatly. incorrect a incorrect. only the mean is likely to change greatly because the mean is not resistant to outliers. the median is resistant to outliers, so the addition of the outlier will not greatly (if at all) change the medians value.

Explanation:

The mean is calculated as the sum of all data - points divided by the number of data - points. An outlier, being a value far from the others, can greatly affect the sum and thus the mean. The median is the middle - value when the data is ordered. In a small data - set, while an outlier can change the median in some cases, it is generally resistant to outliers compared to the mean. So, only the mean is likely to change greatly when an outlier is added to a small data - set.

Answer:

B. No, only the mean is likely to change greatly.