Outliers
Outlier: A number in a set of data that is significantly different from the other numbers in the data. It is either much greater or much lower than most of the other numbers.
It may happen due to an error (these should be ignored). However, it may also occur as an important piece of data that should not be ignored as well, such as when someone does very well on a test of very poorly on a test.
Example: Here are the marks received out of 100 on a science assignment: 21, 23, 24, 24, 27, 29, 29, 29, 32, 37, 37, 38, 39, 40, 50, 50, 51, 54, 56, 57, 58, 59, 61, 71, 99
What is the outlier?
Calculate the mean, median, and mode with the outlier and without the outlier.
Outlier: = 99
Mean with outlier: 21 + 23 + 24 + 24 + 27 + 29 + 29 + 29 + 32 + 37 + 37 + 38 + 39 + 40 + 50 + 50 + 51 + 54 + 56 + 57 + 58 + 59 + 61 + 71 + 99 = 1095 divided by how many numbers present which is 25. 1095 divided by 25 = 43.8 Mean with outlier is 43.8
Median with outlier: Find the middle number which is 39
Mode with outlier: Find the most occurring number which is 29
Mean without outlier: Take the sum of the data set with outlier which is 1095 and subtract the outlier, 1095 - 99 = 996 and divide that number by 24 because when we take out the outlier we are left with 24 numbers. 996 divided by 24 = 41.5 Mean without outlier is 41.5
Median without outlier: the data set is now an even number so find the two middle numbers and divide them by 2.
38 + 39 = 77 divided by 2 = 38.5 Median without outlier is 38.5
Mode without outlier would be the same with an outlier. It would still be 29 because it is the most occurring number.
Video on outliers
