Introduction to Statistics
Statistics is a mathematical science including methods of collecting, organizing and analyzing data in such a way that meaningful conclusions can be drawn from them. In general, its investigations and analyses fall into two broad categories called descriptive and inferential statistics.
Descriptive statistics deals with the processing of data without attempting to draw any inferences from it. The data are presented in the form of tables and graphs. The characteristics of the data are described in simple terms. Events that are dealt with include everyday happenings such as accidents, prices of goods, business, incomes, epidemics, sports data, population data.
Inferential statistics is a scientific discipline that uses mathematical tools to make forecasts and projections by analyzing the given data. This is of use to people employed in such fields as engineering, economics, biology, the social sciences, business, agriculture and communications.
Introduction to Population and Sample
A population often consists of a large group of specifically defined elements. For example, the population of a specific country means all the people living within the boundaries of that country.
Usually, it is not possible or practical to measure data for every element of the population under study. We randomly select a small group of elements from the population and call it a sample. Inferences about the population are then made on the basis of several samples.
A company is thinking about buying 50,000 electric batteries from a manufacturer. It will buy the batteries if no more that 1% of the batteries are defective. It is not possible to test each battery in the population of 50,000 batteries since it takes time and costs money. Instead, it will select few samples of 500 batteries each and test them for defects. The results of these tests will then be used to estimate the percentage of defective batteries in the population.
Quantitative and Qualitative Data
Data is quantitative if the observations or measurements made on a given variable of a sample or population have numerical values.
Example: height, weight, number of children, blood pressure, current, voltage.
Data is qualitative if words, groups and categories represents the observations or measurements.
Example: colors, yes-no answers, blood group.
Quantitative data is discrete if the corresponding data values take discrete values and it is continuous if the data values take continuous values.
Example of discrete data: number of children, number of cars.
Example of continuous data: speed, distance, time, pressure.
Probability Questions with Solutions.
More references on elementary statistics and probabilities.