AQA A Level Maths: Statistics復習筆記2.3.1 Outliers & Cleaning Data
Outliers
What are outliers?
- Outliers are extreme data values that do not fit with the general pattern of the data
- They can come from one or two extreme events or from mistakes in the data collection
- Outliers will affect some statistics that are calculated from the data
- They can have a big effect on the mean, but not on the median or usually the mode
- The range will be completely changed by a single outlier, but the interquartile range will not be affected
- When calculating the mean or the range it is important to decide whether the outlier(s) should be included in the calculations
- The question will tell you whether to include the outliers or not
- You may have to decide which value is the outlier to be removed
- In general outliers are included if they are a valid piece of data and excluded if it is likely that they are erroneous
How are outliers calculated?
- Most of the time within this syllabus the outliers will be a particular distance either side of the?interquartile range
- The most common way to calculate an outlier will be using the formulae:
How are outliers represented on box plots?
- On a box plot an outlier is represented as a cross either side of the maximum or minimum value
- If the maximum or minimum value is discovered to be an outlier, the?new?maximum or minimum value will need to be found for the box plot
- If the data value just above the minimum or just below the maximum is known, this will become the new value
- If the data value is not known, the new minimum or maximum will become the outlier boundary
Cleaning Data
When should data be cleaned?
- The cause of the outlier should be examined by looking into the context of the data
- For example:
- a test score of over 100% would most likely be a data collection error
- a single salary that is much higher than the others would likely be for the CEO of the company
- If an outlier is determined to be from an error in data collection it should be removed from the data.
- Removing the incorrect data value(s) is called?cleaning the data
- It is important to consider very carefully whether you should remove the data value or not
- If the data value is not an error it should not be removed from the data
- If a data value is removed from the data set before calculations are carried out, a justification for the removal of the outlier must be made
- Cleaning data also involves removing missing data and errors
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,
(i)Identify any outliers within the data set.(ii)Clean the data by deciding which values should be removed, justify your answer.
Exam Tip
- Read the question carefully to determine which type of outlier you should be finding and to make sure you are using the correct method.
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