**Statistics**

is the field of Mathematics that collects, organizes, analyses, and interprets data.*Statistics*is also the term used for the data.*Statistics*- When determining what is to be studied, it is important to know what the
to be studied is.*population* - Is it going to be all cats, all long haired cats, or all curly haired dogs?
- To study the whole population you would use a
.*census* - However, most of the time, the population is too large, so a sample is chosen. A
will be a subset of the whole population. There are several different Sampling Techniques.*sample* *Cluster**Convenience**Random**Stratified**Systematic*- .
- The data that is collected will be of two different
.*Data Types* : names & similar*Qualitative Data*: numbers, which can be discrete (only particular numbers) or continuous (any real number value).*Quantitative Data*- Data can be further sorted into
:*Levels of Measurement* : data can only be categorized, i.e. named*Nominal*: data can be ordered or ranked*Ordinal*: data can be used for calculations, zero does not mean 'none'.*Interval*: data can be used for calculations, cannot be negative, zero means 'none'.*Ratio*- Videos on Data Types and Levels of Measurement are on the Data Types page.
- Now the data can be organized and displayed using a variety of methods:
is a chart which includes how many(frequency) of each piece of data*Frequency Distribution*- A
is a bar chart displaying the frequency on the vertical, with the classes on the horizontal*histogram* - A
is a line graph, similar to the histogram. Often the ends of the graph are connected to the x-axis.*frequency polygon* - A
is a circular graph, often used for comparing parts of the data to all of the data.*pie chart* - A
is a chart which lists each piece of data*Stem and Leaf Display* - Videos on Charting and Graphing Data are on the Graphing Data page.
- Where is one value in relation to the rest of the data?
- When you have a lot of data, normally over 100 pieces of data, sorting it into
may be a good idea. The data will be divided into 100 sections (percent = per 100). We often see this with nationwide Statistics, like a child's height in the 65th percentile.*percentiles* - Similar to percentiles,
are good for large amounts of data, but can also be useful when there is under 100 pieces of data. The quartiles are found by finding the median of all the data (Q2), then the medians of the 'halves' of data (Q1 & Q3).*quartiles* - The main 'averages' are the mean, median, mode, and midrange. The Mean and Median are terms most people are familiar with.
- The
is the arithmetic average, where you add all your pieces of data and divide by how many there are.*Mean* - The
is the physical middle of the data.*Median* - The
is the piece of data that occurs most often.*Mode* - The
is when you take the smallest & largest and only 'average' those 2.*Midrange* - When you want to know how far a piece of data is from the mean, the
is the calculation you need. This calculation with the Empirical Rule will help you keep track of how much of the data is within a certain 'distance' from the mean.*Standard Deviation* - Another tricky but useful calculation, is the
, r. When r is close to 1 or -1 there may be a relation bewteen the two variables, when it is close to 0 there is no relation between them. Do not confuse relation with cause and effect.*Correlation Coefficient* - Videos on these calculations are on the Relational Calculations page.

Definitions and Formula are from numerous years of teaching the topics, but have recently been double checked with:

Borowski, E. J., & Borwein, J. M. (2006). *Collins Web-linked dictionary of mathematics*. New York, NY: HarperCollins Pub.