1. 20/05/2015 Skew

2. 20/05/2015 Skewness

3. 20/05/2015 Examining Skewness 1. Compare the mode, median and mean against each other Symmetrical:mean = median = mode Positive skew:mode < median < mean Negative skew:mean < median < mode

4. 20/05/2015 Examining Skewness 2. Use quartiles Symmetrical Positive skew Q1Q1 Q2Q2 Q3Q3 Q1Q1 Q2Q2 Q3Q3 Q1Q1 Q2Q2 Q3Q3 Negative skew

5. 20/05/2015 Examining Skewness 3. Use a measure of skewness to calculate its value Skewness = 3 (mean – median) Standard deviation Advantages? Pearson’s Coefficient of Skewness

6. 20/05/2015 Outliers/Extreme Values It is important to identify outliers (extreme values) to make box plots more informative

7. 20/05/2015 Identifying outliers for drawing box plots The whiskers are now not necessarily the minimum and maximum values Q1Q1 Q2Q2 Q3Q3 Q 1 – 1.5 x IQRQ 3 + 1.5 xIQR xx x Or min value Or max value