Statistics and Probability CLAST Review Workshop Statistics and Probability 4. Identifying Relationships Among Mean, Median, and Mode (skill II D 1)

Data Distributions Symmetrical Data Distribution Normal Distribution Skewed (or Asymmetrical) Data Distribution Skewed Right Skewed Left 11/14/2018 Dave Saha, Kathy Lyden

Data Distribution Basics Mode - 70 and 90 element that occurs most frequently highest point on the graph may be modal, multi-modal, or non-modal Median - 80 the middle value of all the data Mean - 80 arithmetic average Example 60 70 80 90 100 11/14/2018 Dave Saha, Kathy Lyden

Symmetrical Data Distribution with Central Peak Example one mode highest point on the graph is at the center mode = mean = median right and left halves of the graph are mirror images of each other 60 70 80 90 100 11/14/2018 Dave Saha, Kathy Lyden

Normal Distribution Example One of the most important distributions in statistics 50 60 70 80 90 100 110 11/14/2018 Dave Saha, Kathy Lyden

Skewed Data Distribution Examples Mode is still the highest part of the graph. Mean tends to be pulled by the tail more than the median. Skewed Right tail is pulled to the right mean is greater than the median Skewed Left tail is pulled to the left mean is less than the median 11/14/2018 Dave Saha, Kathy Lyden

Skewed Data Distribution Example If the mode represents more than half of the data, then the mode equals the median. 11/14/2018 Dave Saha, Kathy Lyden