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Experiments and Variables in Statistics Help

By — McGraw-Hill Professional
Updated on Oct 25, 2011

Introduction to Experiments and Variables in Statistics

If you want to understand anything about a scientific discipline, you must know the terminology. Statistics is no exception. This section defines some of the most common terms used in statistics.

Statistics is the analysis of information. In particular, statistics is concerned with data : information expressed as measurable or observable quantities. Statistical data is usually obtained by looking at the real world or universe, although it can also be generated by computers in “artificial worlds.”

Experiment

In statistics, an experiment is an act of collecting data with the intent of learning or discovering something. For example, we might conduct an experiment to determine the most popular channels for frequency-modulation (FM) radio broadcast stations whose transmitters are located in American towns having less than 5000 people. Or we might conduct an experiment to determine the lowest barometric pressures inside the eyes of all the Atlantic hurricanes that take place during the next 10 years.

Experiments often, but not always, require specialized instruments to measure quantities. If we conduct an experiment to figure out the average test scores of high-school seniors in Wyoming who take a certain standardized test at the end of this school year, the only things we need are the time, energy, and willingness to collect the data. But a measurement of the minimum pressure inside the eye of a hurricane requires sophisticated hardware in addition to time, energy, and courage.

Variable (In General)

In mathematics, a variable , also called an unknown , is a quantity whose value is not necessarily specified, but that can be determined according to certain rules. Mathematical variables are expressed using italicized letters of the alphabet, usually in lowercase. For example, in the expression x + y + z = 5, the letters x , y , and z are variables that represent numbers.

In statistics, variables are similar to those in mathematics. But there are some subtle distinctions. Perhaps most important is this: In statistics, a variable is always associated with one or more experiments.

Discrete Variable

In statistics, a discrete variable is a variable that can attain only specific values. The number of possible values is countable. Discrete variables are like the channels of a television set or digital broadcast receiver. It’s easy to express the value of a discrete variable, because it can be assumed exact.

When a disc jockey says “This is radio 97.1,” it means that the assigned channel center is at a frequency of 97.1 megahertz, where a megahertz (MHz) represents a million cycles per second. The assigned channels in the FM broadcast band are separated by an increment (minimum difference) of 0.2 MHz. The next lower channel from 97.1 MHz is at 96.9 MHz, and the next higher one is at 97.3 MHz. There is no “in between.” No two channels can be closer together than 0.2 MHz in the set of assigned standard FM broadcast channels in the United States. The lowest channel is at 88.1 MHz and the highest is at 107.9 MHz (Fig. 7-1).

A Statistics Sampler DISCRETE VARIABLE

Fig. 7-1. The individual channels in the FM broadcast band constitute values of a discrete variable.

Other examples of discrete variables are:

  • The number of people voting for each of the various candidates in a political election.
  • The scores of students on a standardized test (expressed as a percentage of correct answers).
  • The number of car drivers caught speeding every day in a certain town.
  • The earned-run averages of pitchers in a baseball league (in runs per 9 innings or 27 outs).

All these quantities can be expressed as exact values.

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