Statistics

Statistics is a branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation. In applying statistics to, for example, a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments. See glossary of probability and statistics.

When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.

Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.

A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a "false positive") and Type II errors (null hypothesis fails to be rejected and an actual difference between populations is missed giving a "false negative"). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.[citation needed]

Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.

Statistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more heavily from calculus and probability theory. In more recent years statistics has relied more on statistical software to produce tests such as descriptive analysis.

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Scholarships for Statistics Majors

Bullet name award deadline Link
 

Regeneron Science Talent Search

Society for Science and the Public

Up to $250,000 November 07, 2024 See Details
 

Regeneron Science Talent Search

Society for Science and the Public

award

Up to $250,000

deadline

November 07, 2024
See Details
 

Edith Nourse Rogers STEM Scholarship

U.S. Department of Veterans Affairs

Up to $30,000 Varies See Details
 

Edith Nourse Rogers STEM Scholarship

U.S. Department of Veterans Affairs

award

Up to $30,000

deadline

Varies
See Details
 

Willard L. Eccles Foundation Graduate Fellowship

Utah State University, College of Science

$18,000 Varies See Details
 

Willard L. Eccles Foundation Graduate Fellowship

Utah State University, College of Science

award

$18,000

deadline

Varies
See Details
 

K-State Math Teacher Scholarship

Kansas State University - College of Education

Up to $18,000 Varies See Details
 

K-State Math Teacher Scholarship

Kansas State University - College of Education

award

Up to $18,000

deadline

Varies
See Details
 

Astronaut Scholarship in Science and Technology

Astronaut Scholarship Foundation

Up to $15,000 Varies See Details
 

Astronaut Scholarship in Science and Technology

Astronaut Scholarship Foundation

award

Up to $15,000

deadline

Varies
See Details
 

Air Force ROTC Express Scholarship

University of Iowa

$15,000 Varies See Details
 

Air Force ROTC Express Scholarship

University of Iowa

award

$15,000

deadline

Varies
See Details
 

Alice P. Gast STEM Scholarship

Lehigh University

$12,500 January 01, 2025 See Details
 

Alice P. Gast STEM Scholarship

Lehigh University

award

$12,500

deadline

January 01, 2025
See Details
 

SEI Native American Education Scholarship

Solar Energy International (SEI)

$10,000 Varies See Details
 

SEI Native American Education Scholarship

Solar Energy International (SEI)

award

$10,000

deadline

Varies
See Details
 

SEI Energy Women in Solar Scholarship

Solar Energy International (SEI)

$10,000 Varies See Details
 

SEI Energy Women in Solar Scholarship

Solar Energy International (SEI)

award

$10,000

deadline

Varies
See Details
 

EAGLES Scholarship - PSU

Portland State University

$10,000 Varies See Details
 

EAGLES Scholarship - PSU

Portland State University

award

$10,000

deadline

Varies
See Details