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What are statistics?
Statistics is the branch of mathematics that describes groups with some shared property. The word, 'statistics' in this use is singular, a single field of study.
Statistics uses group characteristics, such as a group average, to measure something meaningful about a population. (A population in statistics doesn't necessarily mean people, it can be any sort of collection of things.) What statistics attempts is to draw a picture of a group based on the individuals in that group.
Statistics is concerned with the overall picture and we have to be careful not to mistake something from the general statistical picture with any specific example. For instance, the average household in the US has 2.1 children (2006 estimate). Certainly, we don't mean there is a tenth of a kid in anyone's house. In fact, no family at all is average using this statistic alone.
Who invented statistics?
The first use of statistics as a type of applied mathematics is by John Graunt. He was a haberdasher (someone who makes or sells small items used in sewing clothes) who had an interest in demographics. Demographics is the study of human populations- similarities and differences between groups of people. In 1674, he published a book that used statistical methods to analyze some of the data he had collected.
How are statistics used in the real world?
Whenever you read a report about a general issue, the broad picture is usually communicated by way of a statistical measure. Here are some examples:
All of these are calculated by summing and averaging many data points and using statistics to generate one number. The number then gives a broad sense of all the data in combination.
A basic problem using statistics.
If a class of ten calculus students has their IQs measured as 120, 110, 100, 99, 132, 110, 97, 105, 115, and 106, what is the average IQ in that class?
A simple average is calculated by adding up all the data points (IQs) and then dividing by the number of measurements taken. The sum of the ten IQs is 1,094 and this sum, divided by 10 equals the average, 109.4.
An interesting fact about statistics.
Statistics can be misused in an attempt to sway people to a particular point of view. Without an understanding of statistics and the meaning of the mathematics, it may be possible to misinform instead of inform.
Because of this, statistics have gotten a rather poor reputation outside of those familiar with the mathematics. Here are a few quotes:
And here are some ways you may have seen statistics misused yourself: