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Statistics would be defined as follows:
Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data. The mathematical theories behind statistics rely heavily on differential and integral calculus, linear algebra, and probability theory. Statisticians, people who do statistics, are particularly concerned with determining how to draw reliable conclusions about large groups and general events from the behavior and other observable characteristics of small samples. These small samples represent a portion of the large group or a limited number of instances of a general phenomenon.The two major areas of statistics are known as descriptive statistics, which describes the properties of sample and population data, and inferential statistics, which uses those properties to test hypotheses and draw conclusions.
So far, I enjoy writing about the application of calculus in business. However, data gathering is required before a single principle of mathematics is ever executed. The first thing I associated with statistics is the questionnaire. The scientific method involves observation, question, hypothesis, experimentation, conclusion, and result. One of its pioneers was Sir Francis Bacon. In short, statistics is really needed in the scientific method. Data is gathered in every step from observation to the results.
I would think about how statistics' known important areas are (1) state decisions, (2) economics, (3) business management and industry, (4) social and natural sciences, (5) biology and medicine, and (6) research (the most common thing I associate with it). Research would be wrapped around the first five things mentioned. You do research and get data to determine any crucial decision. For example, business calculus requires every data before the slightest derivative or anti-derivative is written. All these data are used in every aspect such as marketing, managerial, technical (which is research and development), and financial. All of these require empirical data (whether descriptive or inferential) to decide on everything.
Good examples of statistics' applications are in making a feasible study and human resources. A feasible study must find whether or not a market is worth entering into with a sample size of 95% accuracy and 5% error. There are some methods known as convenience sampling, random sampling, and purposive sampling. Linear regression analysis will help evaluate trends and forecasts to reduce losses as much as possible. Human resources may benefit from chi-square to compare observed results with observed results. Human resources might need to know their opinion about their managers and supervisors to see if anything needs to be done. These are but a few examples. Take note that I'm not a statistician.
Hotel & Restaurant Management (HRM) which was once regarded as a "loser course" has statistics in the course prospectus. I remembered how HRM students can be seen in group-study to discuss about their statistics exams. The HRM students didn't only have to take economics, accounting, and business calculus. Statistics is also very much required since it takes a lot of good statistics to make a good dish, to determine the peak seasons of hotels and restaurants, and everything related to nailing a good profit.
I think statistics, like economics, also needs to be taught in middle school. I still feel so stupid (until now) when I realized that I didn't understand the role of economics and statistics until I entered college. It practically leaves people clueless when they just study maths and economics just for the grade. What's needed is not just to teach statistics but also how to do statistics in both middle school and high school. Every sound decision is made with statistics on hand, right?
References
https://www.investopedia.com/terms/s/statistics.asp