Mathematics – Probability
As numbers themselves cannot lie, any harm or misunderstanding caused by numbers is the fault of the presenter or interpreter of the numbers. Probability theory and statistics help to describe events with numbers, allowing predictions and forecasts regarding the probability that certain events will occur to be made with a degree of certainty.
Mathematical statistics are used in all the natural sciences, as well as in the scientific study of human society and social relationships.
Mathematics – Statistics
Once election polls have closed, pollsters are able to make relatively precise projections that forecast what the results of the final vote will be. They are able to do this using the tools of statistics.
Descriptive statistics are used to represent collected data. Very large quantities of information about individual events can be summarized according to certain variables in order to represent the data clearly, for example as a graphic display. Once data is collected, a rough list is created in order to identify the characteristics of units in a population. This is dependant on what type of information is sought.
For example, determining the ages of people in a city. A representative sample can be used for a very large population. As each characteristic, in this case an individual’s age, can come up repeatedly, a frequency table is created. The absolute frequency, or the actual counted number of times a characeristic occurs, is used in a frequency table, but the relative frequency is occasionally interesting and meaningful, too.
For example, if 47 of 3,050 inhabitants in a city are 60 years old, the relative frequency of sixty- year-olds in the city is f = 47 = 0.01541, or 1.541 percent.
Evaluation of data
Statistics aims to summarize data with a minimal loss of information. The mean value of the data, or the average of the information collected, is an important parameter of statistics. Statistical spread is the observed difference of individual data from the mean value, which is used to calculate the standard deviation.
When a specific promise cannot be made, such as a company’s cellular battery lasting exactly 70 hours, the company can use testing and statistics to predict that the battery will last 70 hours, give or take five hours.
DATA PRESENTATION
Presenting data as graphic displays is an important component of the field of statistics. However, a certain amount of interpretation may be involved. In preparing the figures, a particular weight must be given to each aspect thus making a truly neutral presentation nearly impossible.
For instance, depending on how the scales are chosen for the x and y axes, a graph of changing values such as unemployment or GDP may appear to be a gradual or steep curve. False impressions can also be created when a portion of an axis is omitted.