Data Analytics Chapter 1 - EDA
What are the types of representation?
Numerical - Continous Data & Discrete Data
Categorial Data - Nominal & Original
Continuous Data
Any data on any Value, no gaps
Continous Data (Interval)
Only differences have meaning, no fixed zero points
- 20 degrees is not twice as hot as 10 degrees
Continous Data (Ratio)
Does have a zero point
- 2km is twice as long as 1 km
Discrete data
Only certain value (integers), has gaps
Categorical data
No numbers as values
- can somtimes have numbers such as value score 1-5, but this is no numerical data (can't calculate with these numbers)
Categorical data (Nominal)
2 or more outcomes that have no natural order
Categorical data (Ordinal)
2 or more outcomes that have a natural order
What are key features of EDA
- Getting to know data before future analysis
- Use graphs
- Generate questions
- Detect errors -> Don't take data for granted
Scatter plots
Used to investigate relations
Mean
The average of values
- Is sensitive to outliers
Median
Odd number of observations
- The middle
- Not sensitive to outliers
Mode
The most frequent value
Percentile
The cut off point for P% of data.
> 1st quartile (Q1): cut off point for 25% of data
> 2nd quartile (Q2): cut off point for 50% of data
> 3rd quartile (Q3): cut off point for 75% of data
Range
Max-Min (sensitive for outliers)
Interquartile range
(IQR) = Q3-Q1
Sample Variance
How much the values differ/vary
- Sensitive to outliers
Sample Standard Deviation
How values are spread out from the average
- Describes variability
- Sensitive to outliers
Median Absolute Deviation
Median of the absolute deviation from the median.
- The higher the above statisitcs are, the more spread/variability there is in the data
Standardization (= z-score normalization)
Transforms data into universal statisical unit of standard deviation from the mean.
- Negative z-score: Value is below mean
- Positive z-score: Value is above mean
Standardization - Rule of thumb
Observations with a z-score larger than 2.5 are considered to be outliers.
Association statisitve: using scatter plots
Captures how strong the relation between two quantities is.
- Positive assossiation -> Higher budget = Higher profit
- Negative assossiation ->Lower budget = Lower profit
Sample Covariance
Must be scaled into sample correlation to be useful
Sample Correlation
- 'No' relation = r(xy) close to 0
- 'Perfect' relation = r(xy) close to -1 or +1
Correlation
Only measures the strength of linear relations
How many peaks does Unimodal distribution have?
1 peak
How many peaks does Bimodal distribution have?
2 peaks
How many peaks does Multimodal distribution have?
More than 2 peaks
How to prove symmetric distribution
Mean = Median
When is a graph right-skewed?
mean > median
When is a graph left skewed?
mean < median
Box-and-Whisker Plot (Boxplot)
- Shows the summary statistics of subets of a data.
- Great to compare groups, but not show the shape of the data
Violin Plot
- Combination of boxplot and density plot
- The thickness of the violin shows the amount of data for the corresponding y-value
What is ECDF
- Empirical Cumulative Distribution Function
- A function that for a given value (x) returns the fraction of observations that are equal to or smaller than x.
- There are no bins, data speaks for itself
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