1. Chapter 3.3 Quartiles and Outliers

2. Interquartile Range  The interquartile range (IQR) is defined as the difference between Q 1 and Q 3  It is the range of the middle 50% of the data  It can be used as a rough measurement of variability  It can be used to identify outliers

3. Find the interquartile range:  2, 3, 5, 6, 8, 10, 12, 15, 18, 20

4. Deciles  Deciles divide the distribution into 10 groups  Denoted by D 1, D 2, etc….  D 1 corresponds to the 10 th percentile  D 5 corresponds to the median  For example: 2, 3, 5, 6, 8, 10, 12, 15, 18

5. Outliers  An outlier is an extremely high or an extremely low data value when compared with the rest of the data values.  An outlier can strongly affect the mean and standard deviation of a variable

6. Steps for Identifying outliers 1. Arrange the data in order and find Q 1 and Q 3 2. Find the interquartile range 3. Multiply the IQR by 1.5 4. Subtract the value obtained in step 3 from Q 1 and add the value to Q 3 5. Check the data set for any data value that is smaller than Q 1 – 1.5(IQR) or larger than Q 3 + 1.5(IQR)

7. Check the following data set for outliers  5, 6, 12, 13, 15, 18, 22, 50  171, 111, 197, 179, 121, 325, 159

8. NFL Salaries  The salaries (in millions of dollars) for 29 NFL teams for the 1999-2000 season are given in this frequency distribution. 1. Find the percentile of values 44, 48, 54 2. Find the values that correspond to the 35 th, 65 th and 85 th percentiles Class boundariesFrequency 39.9-42.82 42.9-45.82 45.9-48.85 48.9-51.85 51.9-54.812 54.9-57.83

9. Try It!  More Practice on Outliers