1. Describing Distributions
3 topics that must be addressed:
Shape
Center
Spread

2. Shape Always describe the basic shape of the distribution.
Symmetric – left and right sides are mirror images, or approximate (since we’re dealing with real data)

3. Skewed Left – majority of the data is on the right side but trails out to the left
Skewed Right – majority of the data is on the left side but trails out to the right

4. Unimodal – one major mode where the data is collected around
Bimodal – two major modes
Multimodal – multiple modes
Uniform – data is flat

5. Also mention any unusual features
Outliers – observations away from the main distribution.
Gaps- Spaces between
clumps of data

6. Center Spread Mean or Median Right now, just approximate
Will use either Std. deviation or IQR (will learn later)
Always list the range of the data (min, max).

7. Example
The distribution is unimodal and skewed to the right. The center is around 15. The range is (0, 60). There is a gap in the 55 to 60 bin.
The distribution is unimodal and approximately symmetric. The center is around 5 or 6. The range is (0, 17). There is a possible outlier at 16.

8. Practice – Describe the Distribution
Symmetric and Unimodal
Center is around 475
Most of the data is spread between 325 to 675

9. Practice – Describe the Distribution
Skewed right and Unimodal
The center is around 30 to 40
Most of the data is spread between 5 and 50 with a long tail out to 185

10. Practice – Describe the Distribution
Skewed to the left and unimodal
There may be some outliers around 53 and 55.
The center is around 90
Most of the data lies between 80 and 100

11. Practice – Describe the Distribution
Skewed to the right (though approximately symmetric might be alright here) and Unimodal
The center is around 22-23
Most of the data lies between 15 and 31

12. Practice – Describe the Distribution
Skewed to the right and unimodal
There is an outlier between 280 and 300
There is a small gap at 150
The center is around 50
Most of the data lies between 0 and 80

13. Practice – Describe the Distribution
Skewed to the Right
Bimodal with one peak at 120 and another smaller one at 350
Possible outlier at 510
The overall center is around 200. The center of the first cluster is around 150 and the second smaller cluster is around 350.
Most of the data is spread 50 to 225 and then there is another smaller cluster between 270 to 400.