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

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

3. 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
11/14/2018
Dave Saha, Kathy Lyden

4. 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
11/14/2018
Dave Saha, Kathy Lyden

5. Normal Distribution
Example
One of the most important distributions in statistics
11/14/2018
Dave Saha, Kathy Lyden

6. 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

7. 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