1. Tips
1.1. Always see them graphically, numeric summary dont tell everything
1.1.1. shapes
1.1.2. trends
1.1.3. gaps
2. Data Types
2.1. Categorical/Qualitative
2.1.1. No sense of ordering or difference in importance
2.1.2. Classify/Label
2.1.3. E.g.
2.1.3.1. Gender
2.1.3.2. Products
2.2. Numerical/Quantitative
2.2.1. Types
2.2.1.1. Continuous
2.2.1.1.1. Measured
2.2.1.1.2. Can take finer granularity
2.2.1.2. Discrete
2.2.1.2.1. Counted
2.2.1.2.2. Whole numbers
2.2.2. Sense of comparability for importance
2.3. So what
2.3.1. Different ways to
2.3.1.1. Collect
2.3.1.2. Analyse
2.3.1.2.1. Control charts
2.3.1.3. Present
2.3.1.4. Interpret
3. Understanding Quantitative data
3.1. Typical value
3.1.1. Based on the distribution or shape of data
3.1.2. Mean
3.1.2.1. Preferred - thats how we think
3.1.3. Median
3.1.3.1. Based on where the data is nor the value
3.1.3.2. Skewed
3.1.3.3. Outliers presented
3.2. data variabily/distance b/n data
3.2.1. S.D
3.2.1.1. affected by outliers
3.2.2. Variance
3.2.3. Relative comparability
3.2.3.1. Coefficient of variation
3.2.4. Quartile ranges
3.2.4.1. not affected by outliers
3.3. Shape
3.3.1. Symmetric/Bell
3.3.2. Modality
3.3.3. Skewness
3.4. Extremes/Oddness
3.4.1. Are they usual
3.4.2. Or something going wrong
4. Histograms
4.1. Size (∴ number) class intervals alter • interpretation • shape • perception of data
4.1.1. Rule of thumb
4.1.2. IQR
4.1.3. make the interval human friendly
4.2. Not recommended for <40 data points
4.2.1. too abstract/rough/cant make sense
4.2.2. alternatives
4.2.2.1. box plot
4.2.2.2. stem and leaf plots
4.3. Why
4.3.1. shape/distribution of data
4.3.1.1. Bell - Shaped
4.3.1.2. Double - Peaked
4.3.1.2.1. bimodal
4.3.1.2.2. combo of two bells
4.3.1.2.3. two data sets
4.3.1.3. Comb
4.3.1.3.1. up down up down
4.3.1.4. Plateau/uniform
4.3.1.5. Skewed
4.3.1.5.1. right
4.3.1.5.2. left
4.3.1.6. Truncated
4.3.1.6.1. no tail on one side
4.3.1.7. Isolated - Peaked
4.3.1.7.1. like double peaked but one set has fewer observations
4.3.1.8. Edge - Peaked
5. Box plot
5.1. box = 50 % data
5.1.1. has both
5.1.1.1. mean
5.1.1.2. mediam
5.2. whiskers
5.2.1. up to 1.5 IQR
5.2.2. if not stops with actual data point
5.3. outliers => cautious interpretation
5.3.1. If the data is long tailed there will be outliers => but they are part of the data and they are not unusual
5.4. Cant tell if there is a bimodality
5.4.1. fat box
5.4.2. short whiskers
5.5. Shape
5.5.1. Look for
5.5.1.1. relative size of left/right boxes
5.5.1.2. length of whiskers
5.5.1.3. side of mean to the median
5.5.1.3.1. mean is pulled towards the skewness of the data
5.5.2. Left/Right Skewed/Symmetric
5.6. Interpretation
5.6.1. Boxes (ignore whiskers) DO overlap
5.6.1.1. no stat. sig. dif
5.6.2. Boxes DONT overlap
5.6.2.1. stat. sig. dif
5.6.2.2. How much stat. dif => Calculate difs in
5.6.2.2.1. Medians
5.6.2.2.2. Means