Apply mathematical analysis to economic and financial information

USING MATHEMATICAL TECHNIQUES TO COLLECT AND ORGANISE DATA
The Concise Oxford Dictionary defines statistics as “Numerical facts systematically collected” and statistic as “Statistical fact or item”.
Statistics entails all aspects of information: collecting, organising, comprehending, communicating, and interpreting.
Definition: Data (singular is datum): things known or assumed as the basis for inference (drawing conclusions) or calculation
The word “Statistics” originally referred to collections of facts (not necessarily numerical) about the State. According to modern usage, however, it refers to collections of numerical facts or estimates and is not restricted to the State.
The word “statistics”, when used in the plural, refers to the figures themselves, suitably classified and tabulated together with any secondary statistics derived from them, such as percentages or averages.
“Statistics”, when used in the singular, refers to the study which deals with the collection, analysis and interpretation of figures. This is also called Statistical Method.
Statistical Method can be broadly divided into two categories, namely descriptive and mathematical statistics:

• Descriptive Statistics. Compiles and presents data exactly as recorded. Descriptive statistics is the most basic form of statistics and lays the foundation for all statistical knowledge
• Mathematical Statistics. Based on the theory of probability, it attempts to draw precise general conclusions from the data

We are going to be focusing on mathematical statistics in the course of this module.

Purpose of statistics
Statistics are all around us. In fact, it would be difficult to go through a full week without using statistics. Imagine watching a football game where no one kept score. The action itself might provide enough excitement to hold your attention for a while, but think of all the drama that would be lost if winning and losing weren’t at issue.
Without statistics we couldn’t plan our budgets, pay our taxes, enjoy games to their fullest, or evaluate performance…
Anyone who manages anything, whether it’s the family budget, a large corporation’s finances or a soccer team, the largest of manufacturing or retail companies, or the smallest of spaza shops, needs statistical information and method for both routine and special purposes, such as the day-to-day running of the business or club, or making new investments.
Both the manager in a large company and the sole proprietor of the corner café require sales statistics in order to detect changes in the pattern of sales, so that they can identify a problem when it occurs and rectify it before it becomes an even bigger problem.
Therefore, the purpose of statistics is not simply to prove a point or satisfy curiosity, but to enable correct decisions to be taken; decisions which are usually based either on comparisons or on estimates.
For example, if we tell our manager that our team has produced 500 tons of a certain product this week, she must have some standard of comparison to tell her if that is satisfactory.
She may know that our team normally produces 600 tons a week, or that our team’s capacity is actually 650 tons a week, or she may be told that another team, with half as many workers, has produced 350 tons this week.
Such comparisons provide information on which action can be taken.

Estimates based on present knowledge are also essential to government and industry alike when formulating plans for the future.
For example, a local authority planning to build a new school must estimate the numbers of children likely to require admission during the next few years.
A manufacturing company deciding whether to build a new plant requires estimates of future demand, as well as knowledge of current trade and production statistics.
Such estimates will be based partly on statistics of population, incomes, regional employment, etc. and partly on a mathematical analysis of past records, while projecting into the future.
The essential function of statistics is control. The team leader does not need statistics to tell him/her what is going on in the workplace- s/he knows the workers, the work going through, when a machine breaks down, etc. However, the manager cannot know it all and depends on the statistics which are supplied to him/her to exercise control and make decisions.
Limitations of statistics
Remember, statistics deal only with the measurable aspects of things and can, therefore, seldom give the complete solution to a problem. They provide a basis for judgment, but not the whole judgment.
More often than not, statistics are used (consciously or subconsciously) to justify decisions that have been reached on other grounds.
Forecasts can sometimes be proved incorrect or invalid by political events, economic crises, new inventions and other unforeseen circumstances.
It is therefore important that the limitations of statistics are understood by both those who compile them and those who use them.