Lesson 5: corrected excerpt

Skewed distributions: mean, median and mode

A corrected version of the Figure 5.07 / 5.08 material, for temporary reference until the module is updated.

What was corrected below

Positively skewed distribution

With positively skewed data, most values cluster towards the lower end, and a small number of unusually high values stretch a long tail out to the right. The mode always sits at the peak. Here, that's on the left. Moving away from the peak into the tail, the mean gets pulled furthest of the three: Mode < Median < Mean.

Positively skewed distribution A right-skewed curve with its peak on the left. Mode sits at the peak, Median further along the shoulder, and Mean furthest right, out in the tail. Mode Median Mean Frequency
Figure 5.07 (corrected). A positively skewed distribution: mode at the peak, mean pulled into the right-hand tail.

Negatively skewed distribution

With negatively skewed data, most values cluster towards the higher end, and a small number of unusually low values stretch a long tail out to the left. The mode again sits at the peak, here on the right. The mean is pulled furthest towards the tail on the low side: Mean < Median < Mode.

Negatively skewed distribution A left-skewed curve with its peak on the right. Mean sits furthest left in the tail, Median further along the shoulder, and Mode at the peak. Mean Median Mode Frequency
Figure 5.08 (corrected). A negatively skewed distribution: mode at the peak, mean pulled into the left-hand tail.
Quick reference
SkewLong tail pointsBulk of data (peak)Order (low to high)
Positive (right)RightLeftMode < Median < Mean
Negative (left)LeftRightMean < Median < Mode
None (symmetric)NoneCentreMean = Median = Mode