Question

Explain the relationships among the mean, median and mode for skewed and symmetric histograms. Illustrate these relationships with graphs?

Answer 1

The below graphs represent the histrograms that are positive skewed, symmetric or normal and negative skewed

Mean Median Mode Median Median Mode Mean Mean- Mode Positive Skew Symmetrical Distribution Negative Skew

For Positive Skewed or Right-tailed distirbution or histogram

As clearly seen from the graph, Mode is less than Median which is less than the Mean

Because there is a tail to the right here, the Mode will be the left of the Mean, the median will be in between Mode and Mean and all these three values will be to the right of the peak in the graph

Mode < Median < Mean or

Mean > Median > Mode

For Symmetrical or Normal histogram

As clearly seen from the graph, Mean is equal to Median which is equal to Mode

Mean = Median = Mode

For Negative Skewed or left-tailed distirbution or histogram

As clearly seen from the graph, Mean is less than Median which is less than the Mode

Because there is a tail to the left here, the Mode will be the right of the Mean and Median, the median will be in between Mode and Mean and all these three values will be to the left of the peak in the graph

Mode > Median > Mean or

Mean < Median < Mode

Summary

Shape	Relationship
Right Skewed or Positive Skewed	Mean > Median > Mode
Symmetrical or Normal	Mean = Median = Mode
Left Skewed or Negative Skewed	Mean < Median < Mode