Foundation of Statistics
Statistics is fundamentally concerned with the presentation and interpretation of chance outcomes that occur in a planned or scientific investigation. Many Statistician, Theorist and Scientist came in different ages; they define the Statistics differently. Some consider statistics as mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data while others consider it a branch of mathematics concerned with collecting and interpreting data. Because of its experimental roots and its focus on applications, statistics is usually considered a distinct mathematical science rather than a branch of mathematics. Some tasks a statistician may involve are less mathematical; for example, ensuring that data collection is undertaken in a way that produces valid conclusions, coding data, or reporting results in ways comprehensible to those who must use them. Statisticians improve data quality by developing specific experiment designs and survey samples. Statistics itself also provides tools for prediction and forecasting the use of data and statistical models. Statistics is applicable to a wide variety of academic disciplines, including natural and socialsciences, government, and business. Statistical consultants can help organizations and companies that don't have in-house expertise relevant to their particular questions. For example, a Statistician wants to record the number of accidents that manly occur from the interaction of E.walnut str and S.Galbstone ave in Jordan valley park, Springfield. The Statistician hoping to justify the installation of traffic lights, he might classify responses in an opinion poll " Yes" or "No". Therefore, the Statistician is usually dealing his data either numerical data or Qualitative data.
In daily life, a person work on different applications and these all have their own progression to have done them. Therefore, working on statistics, it’s important to recognize the different types of data. Data are the actual pieces of information that a person collect through his studies. For example, if a person asks six of his friends how many pets they own, they might give him the following data: 0, 6, 2, 1, 4, 18. Not all data are numbers; let’s say a teacher also record the gender of each of his students, getting the following data: male, male, female, male, female. Most data fall into one of two groups: numerical or Qualitative.
· Numerical data: Statisticians also call numerical data as quantitative data. These data have meaning as a measurement, such as a person’s height, weight, IQ, or blood pressure; or they’re a count, such as the number of stock shares a person owns, how many teeth a dog has, or how many pages you can read of your favourite book before you fall asleep. Numerical data is further broken into two types: discrete and continuous.
o Discrete data it take on possible values that can be listed out. For example, the number of heads in 100 coin flips takes on values from 0 through 100 finite case, but the number of flips needed to get 100 heads takes on values from 100 the fastest scenario on up to infinity. If you never get to that 100th heads, it's possible values are listed as 100, 101, 102, 103, . . . representing the countably infinite case.
o Continuous data represent measurements; their possible values cannot be counted and can only be described using intervals on the real number line. For example, the exact amount of gas purchased at the pump for cars with 20-gallon example tanks would be continuous data from 0 gallons to 20 gallons, represented by the interval [0, 20], inclusive. You might pump 8.40 gallons, or 8.41, or 8.414863 gallons, or any possible number from 0 to 20. In this way, continuous data can be thought of as being unaccountably infinite.
· Qualitative data: When things are grouped accordingly some common property and the number of members of the group are recorded e.g. males/female, vehicle types.
In Statistics there are two statistical methods to collection, presentation, analysis and interpretation of data.
Descriptive Statistics consist of those methods concerned with collection and describing a set of data so as to yield meaningful information. For example, construction of tables, charts, graphs, and other relevant computation in various newspapers and magazine usually fall in the area categorized as descriptive statistics. In the other hand, Statistical Inference comprise those methods concerned with the analysis of a subset of data leading to prediction or inference about the entire set of data.