This packet introduces you to the idea of a boxplot. Some terms that should already be familiar to you are:
- 5 number summary
- outlier
- range
Source: Greene
Here is a good example on creating a 5 number summary. The data is not sorted originally for this problem, so it is helpful to see it being sorted.
Consider the following data set: 13,14, 16, 18, 21, 22, 22, 25, 29, 40
Create a 5 number summary, perform an IQR test to see if there are any outliers, and create a boxplot, making sure to include any outliers.
Source: Greene
13,14, 16, 18, 21, 22, 22, 25, 29, 40
Numbers for 5 number summary:
Min - 13 Q1 - 16 Median - 21.5 Q3 - 25 Max - 40
IQR test:
1. Q3-Q1=IQR 25-16 = 9
2. IQR*1.5 = NUMBER 9*1.5 = 13.5
3. Q3 + NUMBER = upper limit 25+13.5 = 38.5
Q1 - NUMBER = lower limit 16 - 13.5 = 2.5
4. Nothing is less than 2.5, but 40 is greater than the upper limit of 38.5. Therefore, 40 is an outlier.
For the boxplot, you should have an asterisk at 40 to indicate it is an outlier.
Source: Greene