The measure of center that is most affected by outliers is the mean. Let me explain why and give you an example.
The mean is what most people call the average. You find the mean by adding up all the numbers in a set and then dividing by how many numbers there are. Because it uses every number, if there's a really big or really small number in the set (called an outlier), it can change the mean a lot.
The median is the middle number when all the numbers are lined up in order. The mode is the number that appears the most. Neither the median nor the mode is affected much by outliers because they don’t rely on all the numbers in the same way that the mean does.
Example:
Let's look at this set of 10 numbers:
1, 2, 2, 3, 3, 3, 4, 4, 5, 50
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Find the mean:
- Add them all up: 1 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 5 + 50 = 73
- Divide by how many numbers: 73 ÷ 10 = 7.3 (So, the mean is 7.3)
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Find the median:
- First, put the numbers in order: 1, 2, 2, 3, 3, 3, 4, 4, 5, 50
- The middle numbers are the 5th and 6th: 3 and 3
- To find the median, take the average of these two: (3 + 3) ÷ 2 = 3 (So, the median is 3)
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Find the mode:
- The number that appears the most is 3 (it appears 3 times). (So, the mode is 3)
Results:
- Mean: 7.3
- Median: 3
- Mode: 3
As you can see, the mean (7.3) is much higher than the median (3) and the mode (3) because of the outlier (50) in the set. The outlier really pulled the mean up, showing that it is the measure of center most affected by outliers.