The measure of center that is most affected by outliers is the mean. The mean is calculated by adding all the values in a data set and dividing by the number of values. This makes it sensitive to extreme values that are much larger or smaller than the rest of the data set.
For example, let's consider the following data set: 4, 5, 6, 7, 8, 9, 10, 11, 12, 40. The mean of this data set is (4+5+6+7+8+9+10+11+12+40)/10 = 10.2. However, if we add an outlier like 100 to the data set, the mean becomes (4+5+6+7+8+9+10+11+12+40+100)/11 = 19.73. In this case, the outlier drastically changes the value of the mean, making it no longer representative of the central tendency of the data.
On the other hand, the median and mode are less affected by outliers. The median is the middle value when the data is arranged in ascending or descending order, so extreme values do not have as much influence on it. The mode is simply the value that appears most frequently in the data set, and outliers do not have any effect on it.
Statistics Unit Test
15 of 1515 of 15 Items
Question
Of the mean, median, and mode, which measure of center is most affected by outliers? Explain your reasoning including an example with at least 10 data points.(4 points)
3 answers
Make it look like a 4th grader made it
The measure of center that is most affected by outliers is the mean. The mean is when you add up all the numbers and divide by how many numbers there are. If you have a lot of low numbers and one really big number, the mean will be pulled higher because of that really big number.
For example, let's say you have a bunch of numbers: 4, 5, 6, 7, 8, 9, 10, 11, 12, 40. The mean of those numbers is 10.2. But if you add a super big number like 100 to the list, the mean becomes 19.73. That super big number changed the mean a lot!
The median and mode are not as affected by big numbers. The median is just the middle number when you put all the numbers in order, so one big number won't make much difference. The mode is just whichever number shows up the most, so big numbers don't matter.
For example, let's say you have a bunch of numbers: 4, 5, 6, 7, 8, 9, 10, 11, 12, 40. The mean of those numbers is 10.2. But if you add a super big number like 100 to the list, the mean becomes 19.73. That super big number changed the mean a lot!
The median and mode are not as affected by big numbers. The median is just the middle number when you put all the numbers in order, so one big number won't make much difference. The mode is just whichever number shows up the most, so big numbers don't matter.