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

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)

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

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

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

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).

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.

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

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

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

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

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

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.