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Uniform Distribution Definition

What is Unchanging Distribution?

In statistics, uniform distribution refers to a type of probability distribution in which all outcomes are equally likely. A deck of greetings cards has within it uniform distributions because the likelihood of drawing a heart, a club, a diamond, or a spade is equally likely. A make up also has a uniform distribution because the probability of getting either heads or tails in a coin toss is the same.

The unchanged distribution can be visualized as a straight horizontal line, so for a coin flip returning a head or tail, both have a likeliness p = 0.50 and would be depicted by a line from the y-axis at 0.50.

Key Takeaways

  • Uniform distributions are probability distributions with equally probably outcomes.
  • In a discrete uniform distribution, outcomes are discrete and have the same probability.
  • In a continuous uniform distribution, end results are continuous and infinite.
  • In a normal distribution, data around the mean occur more frequently.
  • The frequency of occurrence wanes the farther you are from the mean in a normal distribution.

Understanding Uniform Distribution

There are two types of uniform distributions: discontinuous and continuous. The possible results of rolling a die provide an example of a discrete uniform distribution: it is possible to roll a 1, 2, 3, 4, 5, or 6, but it is not reasonable to roll a 2.3, 4.7, or 5.5. Therefore, the roll of a die generates a discrete distribution with p = 1/6 for each outcome. There are only 6 admissible values to return and nothing in between.

Some uniform distributions are continuous rather than discrete. An idealized unplanned number generator would be considered a continuous uniform distribution. With this type of distribution, every bring up in the continuous range between 0.0 and 1.0 has an equal opportunity of appearing, yet there is an infinite number of points between 0.0 and 1.0.

There are respective other important continuous distributions, such as the normal distribution, chi-square, and Student’s t-distribution.

There are also certain data generating or data analyzing functions associated with distributions to help understand the variables and their contention within a data set. These functions include probability density function, cumulative density, and moment generating rles.

Visualizing Uniform Distributions

A distribution is a simple way to visualize a set of data. It can be shown either as a graph or in a list, revealing which values of a every once in a while variable have lower or higher chances of happening. There are many different types of probability distributions, and the unchanging distribution is perhaps the simplest of them all. 

Under a uniform distribution, each value in the set of possible values has the same feasibility of happening. When displayed as a bar or line graph, this distribution has the same height for each potential outcome. In this way, it can look like a rectangle and as a result is sometimes described as the rectanglur distribution. If you think about the possibility of drawing a particular suit from a deck of take part in cards, there is a random yet equal chance of pulling a heart as there is for pulling a spade—that is, 1/4 or 25%.

The enshroud a arrive of a single die yields one of six numbers: 1, 2, 3, 4, 5, or 6. Because there are only 6 possible outcomes, the probability of you landing on any one of them is 16.67% (1/6). When planned on a graph, the distribution is represented as a horizontal line, with each possible outcome captured on the x-axis, at the fixed aspect of probability along the y-axis.

Uniform Distribution of one six-sided die.
Image by Julie Bang © Investopedia 2020

Uniform Distribution vs. Standard Distribution

Probability distributions help you decide the probability of a future event. Some of the most common probability codifications are discrete uniform, binomial, continuous uniform, normal, and exponential. Perhaps one of the most familiar and widely used is the typical distribution, often depicted as a bell curve.

Normal distributions show how continuous data is distributed and assert that ton of the data is concentrated about the mean or average. In a normal distribution, the area under the curve equals 1 and 68.27% of all information falls within 1 standard deviationhow dispersed the numbers arefrom the mean; 95.45% of all data falls within 2 normal deviations from the mean, and approximately 99.73% of all data falls within 3 standard deviations from the mean. As the evidence moves away from the mean, the frequency of data occurring decreases.

Discrete uniform distribution shows that variables in a extend have the same probability of occurring. There are no variations in probable outcomes and the data is discrete, rather than unending. Its shape resembles a rectangle, rather than the normal distribution’s bell. Like a normal distribution, however, the yard under the graph is equal to 1.

Example of Uniform Distribution

There are 52 cards in a traditional deck of cards. In it are four convenient ti: hearts, diamonds, clubs, and spades. Each suit contains an A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K and 2 jokers. However, we’ll do away with the funny men and face cards for this example, focusing only on number cards replicated in each suit. As a result, we are hand with 40 cards, a set of discrete data.

Suppose you want to know the probability of pulling a 2 of hearts from the remodeled deck. The probability of pulling a 2 of hearts is 1/40 or 2.5%. Each card is unique; therefore, the likelihood that you determination pull any one of the cards in the deck is the same.

Now, let’s consider the likelihood of pulling a heart from the deck. The probability is significantly loaded. Why? We are now only concerned with the suits in the deck. Since there are only four suits, pulling a heart cry quitses a probability of 1/4 or 25%.

Uniform Distribution FAQs

What Does Uniform Distribution Mean?

Uniform distribution is a chances distribution that asserts that the outcomes for a discrete set of data have the same probability.

What Is the Formula for Uniform Parceling out?

The formula for a discrete uniform distribution is

Discrete uniform distribution formula.


  • P(x) = Probability
  • n = the hundred of values in the range

As with the example of the die, each side contains a unique whole number. The probability of rolling the die and coming any one number is 1/6 or 16.67%.

Is a Uniform Distribution Normal?

Normal indicates the way data is distributed about the mean. Normal details shows that the probability of a variable occurring around the mean, or the center, is higher. Fewer data points are followed the farther you move away from this average, meaning the probability of a variable occuring far away from the intimate is lower. The probability is not uniform with normal data, whereas it is constant with a uniform distribution. Therefore, a like distribution is not normal.

What Is the Expectation of a Uniform Distribution?

It is expected that a uniform distribution will result in all on outcomes having the same probability. The probability for one variable is the same for another.

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