Statistics is a branch of mathematics concerned with the collection, organization, analysis, and interpretation of data in order to draw meaningful conclusions. Broadly speaking, statistics is divided into two main areas: descriptive statistics and inferential statistics.
Descriptive statistics focuses on organizing and summarizing data without making predictions or generalizations beyond the data itself. Information is often presented using tables, charts, and graphs. Examples include data related to prices, population, sports results, accidents, and business activity.
Inferential statistics uses mathematical techniques to make predictions, estimates, or decisions about a population based on sample data. This area of statistics is widely used in engineering, economics, biology, social sciences, agriculture, business, and communications.
A population is a complete set of elements being studied. For example, the population of a country includes all people living within its borders.
In many situations, studying every element of a population is impractical or impossible. Instead, a smaller group called a sample is selected, usually at random. Conclusions about the population are then drawn based on information obtained from the sample.
A company plans to purchase 50,000 electric batteries from a manufacturer. The purchase will be made only if no more than 1% of the batteries are defective. Testing all 50,000 batteries would be too costly and time-consuming. Instead, several samples of 500 batteries each are tested. The results are then used to estimate the proportion of defective batteries in the entire population.
Data is quantitative when observations or measurements are expressed numerically.
Examples include height, weight, number of children, blood pressure, current, and voltage.
Data is qualitative when observations are described using words, categories, or labels rather than numbers.
Examples include colors, blood groups, and yes-or-no responses.
Quantitative data can be further classified as discrete or continuous. Discrete data takes specific, countable values, while continuous data can take any value within a range.
Examples of discrete data include the number of children or cars. Examples of continuous data include speed, distance, time, and pressure.
Elementary Statistics and Probability
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