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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.

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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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Variance measures how the data in a given variable distribution are spread relative to the mean. Operationally, it is the average squared distance from the mean and is calculated by the square root of the standard deviation. Conceptually, it indicates how much variation is within a given sample.

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Descriptive statistics are descriptions of the main factors of a group of data or a summary of the information. These statistics give a snapshot of the information that has been gathered. This type of information is often used when there are so many variables in a data cluster that it would be nearly impossible to list or graph every single factor of the information.