IB DP Maths: AA SL復習筆記4.1.5 Outliers
Outliers
What are outliers?
- Outliers are extreme data values that do not fit with the rest of the data
- They are either a lot bigger or a lot smaller than the rest of the data
- Outliers are defined as values that are?more than 1.5 × IQR from the nearest quartile
- x?is an outlier if?x?<?Q1?- 1.5 × IQR?or?x?>?Q3?+ 1.5 × IQR
- Outliers can have a big effect on some statistical measures
Should I remove outliers?
- The decision to remove outliers will?depend on the context
- Outliers?should be removed?if they are found to be?errors
- The data may have been recorded incorrectly
- For example: The number 17 may have been recorded as 71 by mistake
- Outliers?should not be removed?if they are a?valid part of the sample
- The data may need to be checked to verify that it is not an error
- For example: The annual salaries of employees of a business might appear to have an outlier but this could be the director’s salary
Worked Example
The ages, in years, of a number of children attending a birthday party are given below.
2,? ?7,? ?5,? ?4,? ?8,? ?4,? ?6,? ?5,? ?5,? ?29,? ?2,? ?5,? ?13
a)? ? ? ? ?Identify any outliers within the data set.
b)? ? ? ? ? Suggest which value(s) should be removed. Justify your answer.
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