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Q:

# What is p hat in statistics?

A:

The p hat is a symbol which stands for sample proportion. In equations, it is represented as a lower-case p with a small caret above it.

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To understand what the p hat symbol represents and how it is used, the difference between a population and a sample must first be understood. In the study of statistics, the word "population" refers to the entire group that is being studied. A "sample," on the other hand, is only a part of that group. A sample is, ideally, representative of the entire group, meaning that a statistician can study the habits, behaviors and characteristics of that small group and then generalize the findings to the entire population. In statistics, a lower-case p without a caret above it stands for "population proportion." When a statistician calculates the population proportion, the entire group is being factored into the equation.

However, the p hat symbol is used to refer to an even smaller group: a proportion of the sample of the entire group. The p hat is often used when discussing the results of surveys. For example, a statistician asks a sample group of 500 adults if they like grape soda; 342 say yes, 100 say no and 58 have no opinion. The statistician is interested in which proportion like grape soda, so an equation will be formulated to find the p hat, or the proportion that answered "yes." The p hat will then be expressed as a percentage or a fraction of the sample group.

## Related Questions

• A:

Sir Ronald Aylmer Fisher, a British statistician, is considered by many to be the father of the modern science of statistics. The Danish statistician Anders Hald recognized him as a genius who built the foundations for modern statistical science, according to Wikipedia.

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Statistics is the study of numerical information, which is called data. People use statistics as tools to understand information. Learning to understand statistics helps a person react intelligently to statistical claims. Statistics are used in the fields of business, math, economics, accounting, banking, government, astronomy, and the natural and social sciences.

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According to San Jose State University, statistics helps researchers make inferences about data. Instead of just using raw data to explain observations, researchers use various statistical analyses to derive predictions and trends from large data sets. Scientists and professionals use statistics in a variety of disciplines and fields, including biological sciences, political science and engineering.