Describing Distributions

Refer to Khan academy: Example: Describing a distribution

Shapes: Normal, Left Skewed, Right Skewed

Refer to Khan academy: Classifying shapes of distributions

• Normal Distribution (Symmetric distribution)
• Left Skewed Distribution
• Right Skewed Distribution
• Uniform
• Bimodal Distribution

Example

Spread: Range, IQR, Standard Deviation, MAD

Refer to Crash course: Measures of Spread: Crash Course Statistics #4

• Range: (Highest value - Lowest value)
• IQR: (Q3-Q1)
• Standard Deviation: σ (sigma)
• Mean absolute deviation (MAD)

Centres: Mean, Median, Mode

Refer to Crash course: Mean, Median, and Mode: Measures of Central Tendency: Crash Course Statistics #3

• Mean is just an average of all numbers listed.
• Median is the middle positioned number in a ordered number set (means no duplicates). If there're two middles, then average them to get a median number.
• Mode is the number shows up most times in a list.

Outliers

Refer to Khan academy: Judging outliers in a dataset

In statistics, an outlier is an observation point that is distant from other observations.
That being said, outliers in a graph are the MINORITY of the values.

Statistical definition (1.5·IQR Rule)

Outliers are the value fall out of the Fence, which the Upper fence and Lower fence are:

How to choose proper methods

We got different ways to describe the spread, centre and deviation, so we need some strategy to decide which one to use in different cases.

• For Normal Distribution: we use Mean as centre, Standard Variance as spread
• For Skewed Distribution: we use Median as centre, IQR as spread