The measure of center most affected by outliers is the mean. The mean is calculated by adding all the numbers together and dividing by how many numbers there are. When you have a really big or really small number (an outlier), it can make the mean much higher or lower than most of the numbers.
For example, imagine these 10 test scores:
85, 87, 90, 88, 84, 86, 89, 92, 91, 10 (the outlier)
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First, let's find the mean:
- Add them up: 85 + 87 + 90 + 88 + 84 + 86 + 89 + 92 + 91 + 10 = 1002
- Divide by 10 (the number of scores): 1002 ÷ 10 = 100.2
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Now, let's find the median (the middle number when they are in order):
- In order: 10, 84, 85, 86, 87, 88, 89, 90, 91, 92
- The middle numbers are 87 and 88. So, the median is (87 + 88) ÷ 2 = 87.5.
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And the mode (the most common number):
- All numbers are different, so there is no mode.
Here, the mean (100.2) is much higher because of the outlier (10), while the median (87.5) is more like the other scores. So, the mean is most affected by outliers!