Introduction To Statistics

Thursday, 20 June 2019

2:39 PM

MATH2099 Musings Introduction to Statistics 2019-0605 Introduction to Statistics Statistics is the science of the collection, processing, analysis and interpretation of data. Okay cool. Statistics allows us to gain insights into the behaviour of many things, and helps to inform us in future decision making. It considers entropy - that is randornness, uncertainty and variation - all of which are evident in real life. A general overview of an experiment • Aim • Hypothesis • Collection of control data • Collection of experimental data • Inerpretation and inference ot results Terminology • Population - the total collection of elements • Individuals Units - the elements • Variable - A quantitative or qualitative characteristic • Sample - a subset ot the population (part ot all the data) Variables There are two types of variables. • Qualitative (categorical) - ie gender, hair colour • Quantitative (numerical) - ie height, age, salary Note: Some categorical variables may be represented as numeric values - but they are still categorical values Sampling - Picking a good sample If a sample was taken from a population, the sample must be representative of the whole population. Otherwise the sample data would would be biased, a represent a skewed set of data that does not accurately reflect the population, To achieve a good sample, random sampling must be performed The selection of individuals is based upon a totally random tashion. Bur wHaT is rAnDoM Random is the absence ot order But probably most •random' outcomes are based on some complicated pattern we simply just are not aware of We could, however, scope the sample data it we want statistical analysis ot individuals of a certain criteria, or group. Do keep in mind though, that the information produced does not represent the entire population but only that group. (obviously) Graphical Representation of Data Any good statistical analysis of data should always begin with plotting of the data An outlier is an anomaly where a piece of data is extremely different to others Dot plot A dot plot is a summary of numerical data when the data set is small. Each observation is represented by a dot above its corresponding location on a horizontal scale, A second occurance of that same value is stacked on top ot the dot. 0 2 3 4 6 7 e 9 10 11 12 Minutes TO Eat Breakfast IT'S JUST A HISTOGRAM Stem-and-Leaf plot Each observation is separated into a step (all but last digit) and a leaf (last digit), All unique stems are written in a vertical column (smallest at the top), and the leaves corresponding to that stem are Mitten out horizontally (in increasing order) Stem 4 6 8 9 10 Leaf 4679 34688 2256 148 These sort of plots enable us to observe: • Identification of a typical value • Spread of typical values • Presence of gaps • Extent of symmetry • Number and location of peaks • Presence of outliers Stem and leaf plots can be modified to achieve extended needs • Rounding, truncating - simplify detail • Splitting each stem - further distribution detail • Back-to-back stem plots to compare two sets of related distributions Frequency distribution charts, bar graphs, histograms Yeah eh. For histograms of numerically continuous data classes need to be created to group values. These classes are non-overlapping intervals, each (usually) equal in size. Terminology: • symmetric • skewed to the left/right - has a left/right tail • unimodal / bimodal I trimodal I n peaks • bell-shaped - symmetrical and unimodal Class widths do not have to necessarily be equal, as sometimes it is nonsensical Density histograms The area of the a class should be proportional to its frequencies. Density = relative frequency / class width Relative frequency frequncy of the class / total observations There are actually heaps of different types of graphs that we could use. Check out this site' Prev Powered by Hugo I Theme - Even 0 2019 Andrew Wong (75206677) Next 91

 

 

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