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When someone mentions the word statistics in some informative results such as in "Statistics show that 90% of the population are..." or "Results show that only half of those surveyed are...", he or she is concerned about the results of statistical analysis. That is statistics in common usage; it is the summarized results derived from initial data. Statistics as a discipline is concerned much more: it is the painstaking and computation-heavy analysis that precedes the conclusions and the generation of additional implications after results are made.
(1) Data collection - Data is often collected from what we call samples (the subjects for a statistical study) and samples are selected properly through what we call sampling methods. It would be more desirable to use the entire population as the subject for study, but as there are severe constraints to analyzing the entire population (one of which is sheer size), statisticians would be satisfied with samples. Samples are usually people, but they can be objects. Sampling methods are classified as probability sampling methods (where the probability of each member of the population to participate in the study can be calculated) and non-probability sampling methods (any sampling method where the probability of each participant to be chosen in the sample cannot be calculated)
Many think that data collection is as simple as asking the respondents a few questions about a survey. That is far from actual statistical practice. While this dimension of statistics is not mentioned in statistics textbooks, it is often mentioned in research textbooks. Apparatus (such as questionnaires, survey sheets, and interviews) should be as reliable as possible so that they can extract data from the sample as completely and accurately as possible. Ideally, there should be no bias in data collection; and all intentional biases should have a rationale behind it.
(2) Data organization - It is concerned with the most efficient way to present data, as in graphs, charts, tables, or diagrams. Some graphs serve a definite purpose. Bar graphs, for instance, show the respective quantities of discrete objects through bar lengths. Pie graphs show quantities and percentages through proportional sectors of a circle.
(3) Data interpretation - This is the where all the formulae of statistical analysis are used. Data interpretation depends on the type of conclusions sought. Here two other divisions of statistics should be examined. Descriptive statistics concerns itself with the general attributes of the data being studied. It is just showing the characteristics of the given data. Examples include getting the measures of distribution (frequency distribution, histogram, stem-and-leaf plotting), measures of central tendency (mean, median, mode), and measures of dispersion (e.g. range and standard deviation). Inferential statistics concerns itself with deriving conclusions beyond the given data. Remember that most statistical studies use samples instead of entire populations.
Inferential statistics is used, given the data from the sample, to make conclusions about the general population where the sample comes from. The most common inferential statistics methods are t-test, ANOVA (analysis of variance), regression analysis, and chi-square analysis. Statistics has plenty of real-world applications, the most common of which is interpreting scores and conducting surveys:
Interpreting scores include plenty of descriptive statistics, like this: mean - average score; median - the score where there are equal quantities of scores higher and lower than that score; mode - the most frequently occurring score; range - the difference between the highest and lowest score; and standard deviation - a measure of how 'stable' the scores are, or how far apart the scores are from the mean.
Surveying often requires massive amounts of descriptive and inferential statistics. Furthermore, there should be extra sensitivity in selecting respondents and organizing survey results so that the conclusions derived from statistical analysis will be as impartial as possible.