Edge(X) Notes: Module 2 Visualising Distributions Visualising Continuous Data: - The pattern of variability we see is called the distribution of the variable and this pattern typically involves a central tendency, where observations tend to gather around a central value, with fewer observations further away. - We will be interested in describing three main aspects of the distribution we see: o The location or centre of the variability, a typical value taken by the variable. o The spread of the variability, how far the values extend from the centre. o The shape of the variability in whether values are spread symmetrically on either side of the centre. - We will then look for values or patterns which don't match this general description. For example, we may find outliers, values which don't match the rest of the pattern, or bimodal distributions where there may be two distributions of variability in our values. - Continuous variables can be explored using plots such as; o Dot plots: To make dot plots an axis is dram for the chosen variable, and a dot in placed for each response. E.g. height o Histograms o Density plots - With multiple dots that overlap in dots plots, it doesn't much insight. Hence, there are ways to give more detail; o Alpha Bending: This gives each point transparency so overlapping points can be seen o Jitter: In the case where data is still too dense points can be jittered, where points are separated . 150 160 170 180 Height (cm) 190 200 - When there is a lot of data, it can be more useful to present a summary of the data instead in the form of a histogram. In a histogram, multiple ranges are used to fit data for a variable.
- Histograms are a useful tool for the density of a distribution, especially for large data sets. - When there are two peaks within a histogram, that refers to a bimodal distribution 30 Percent of Total 20 10 0 - 150 160 170 180 190 200 Height (cm) - A plot that allows continuous control is a density plot. A density plot works by creating a little lump over each value and then adding the heights of all those lumps together to get an overall curve. - Density plots are also useful for comparing distributions Density 50 60 70 80 90 Mass (kg) 100 110 120 Categorical Variables: - Summarising the distribution of a categorical variable is very simple. All of the observations in each category is tallied up and divided by the total number of observations in each count. This gives the sample proportions in each category. - To display the distribution of a categorical variable we make a bar chart of the proportions. - For a nominal variable there is no ordering of the categories. However, for an ordinal variable, such as age group, we would order the categories as appropriate. E.g. Bar Chart
Spinach Sausage Prawns Pineapple Mushroom 0.00 0.05 Quantiles 0.10 0.15