# 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.

* Description and images provided by Wikipedia under CC-BY-SA 3.0 license .

## Scholarships for Statistics Majors

### SMART Scholarship

Department of Defense

Up to \$38,000 December 01, 2020

### SMART Scholarship

Department of Defense

award

Up to \$38,000

December 01, 2020

### Willard L. Eccles Foundation Graduate Fellowship

Utah State University, College of Science

\$18,000 Varies

### Willard L. Eccles Foundation Graduate Fellowship

Utah State University, College of Science

award

\$18,000

Varies

### Air Force ROTC Express Scholarship

University of Iowa

\$15,000 Varies

### Air Force ROTC Express Scholarship

University of Iowa

award

\$15,000

Varies

### Keynote Scholarship

National Space Club

\$10,000 December 02, 2020

### Keynote Scholarship

National Space Club

award

\$10,000

December 02, 2020

### Edison Scholars Program

Edison International

\$10,000 December 16, 2020

### Edison Scholars Program

Edison International

award

\$10,000

December 16, 2020

### FIRST Scholarship - Rice University

FIRST

\$10,000 February 12, 2021

### FIRST Scholarship - Rice University

FIRST

award

\$10,000

February 12, 2021

### Barry Goldwater Scholarship

Idaho State University

Up to \$7,000 Varies

### Barry Goldwater Scholarship

Idaho State University

award

Up to \$7,000

Varies

### Math Advantage Scholarship - University of Montana, Montana Tech

University of Montana at Montana Tech

\$6,700 Varies

### Math Advantage Scholarship - University of Montana, Montana Tech

University of Montana at Montana Tech

award

\$6,700

Varies

### Montana Minds Scholarship - University of Montana, Montana Tech

University of Montana at Montana Tech

\$6,000 Varies

### Montana Minds Scholarship - University of Montana, Montana Tech

University of Montana at Montana Tech

award

\$6,000

Varies

### Glen E. Ullyot Scholarship

University of Minnesota, Twin Cities

\$6,000 Varies

### Glen E. Ullyot Scholarship

University of Minnesota, Twin Cities

award

\$6,000