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 roger’s claim correct?

No, Roger’s claim is not correct. Only the mean is very likely to change greatly when an outlier is added to a small data set; the median usually changes little or not at all.

Why the mean changes a lot

• The mean uses every value in the data: you add all numbers and divide by how many there are.

• In a small data set, adding one very large or very small outlier drastically changes the sum, so the mean can jump up or down a lot.

• Example idea: in a set like 2, 3, 4, adding 100 makes the average much bigger because 100 dominates the total.

Why the median usually doesn’t

• The median depends on the position (middle value in order), not the size of the extreme value.

• Adding an outlier to one end of the list usually just tacks it onto the beginning or end and does not move the middle value, so the median often stays the same or changes only slightly.

• Because of this, the median is called more “resistant” to outliers than the mean.

Final verdict on Roger

• The correct statement is: only the mean is likely to change greatly when an outlier is added to a small data set.

• So the best answer to the question is: “No, only the mean is likely to change greatly.”

Information gathered from public forums or data available on the internet and portrayed here.