what is uniform distribution 
in statistics uniform distribution refers to a type of probability distribution in which all outcomes are equally likely probability distributions can help you decide the probability of a future event uniform distribution for a deck of cards is expected because the likelihood of drawing a heart a club a diamond or a spade is equally likely a coin also has a uniform distribution expectation because the odds of getting either heads or tails front or back of the coin in a coin toss are the same a uniform distribution can be visualized as a straight horizontal line for a coin flip heads or tails each has a probability of occurring 50 of the time p 0 50 and would be plotted on a chart with a line from the y axis at 0 50 understanding uniform distributionthere are two types of uniform distributions discrete 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 possible to roll a 2 3 4 7 or 5 5 therefore the roll of a die generates a discrete distribution with the probability of 1 6 for each outcome there are only 6 possible values to return and nothing in between the possibilities are finite on the other hand continuous uniform distributions have infinite distribution possibilities an idealized random number generator would be considered a continuous uniform distribution with this type of distribution every point 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 several other important continuous distributions such as the normal distribution chi square and student s t distribution there are also several data generating or data analyzing functions associated with distributions that help explain the variables and their variance within a data set these functions include probability density function cumulative density and moment generating functions the term discrete in statistics refers to variables with singular countable and limited possible values visualizing uniform distributionsa distribution is a simple way to visualize a set of data it can be shown either as a graph or a list and reveals which values of a random variable have lower or higher chances of happening the uniform distribution is perhaps the simplest of all probability distributions in a uniform distribution each value in the set of possible values has the same possibility 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 therefore is sometimes described as the rectangular distribution if you think about the possibility of drawing a particular suit from a deck of playing 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 roll of a 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 plotted on a graph the distribution is represented as a horizontal line with each possible outcome captured on the x axis at the fixed point of probability along the y axis example of uniform distributionthere are 52 cards in a traditional deck of cards also in that deck are four suits hearts diamonds clubs and spades each suit contains an a 2 3 4 5 6 7 8 9 10 j q k the deck contains 2 jokers as well however we ll ignore the jokers and face cards for this example and focus only on number cards replicated in each suit as a result we are left with 40 cards a set of discrete data suppose you want to know the probability of pulling a 2 of hearts from the modified deck the probability of pulling a 2 of hearts is 1 40 or 2 5 each card is unique therefore the likelihood that you will 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 higher why we are now only concerned with the suits in the deck since there are only four suits pulling a heart yields a probability of 1 4 or 25 the plotted results from rolling a die will be discretely uniform whereas the plotted results averages from a roll of dice more than one die will be normally distributed uniform distribution vs normal distributionsome of the most common probability distributions are perhaps one of the most familiar and widely used is the normal distribution often depicted as a bell curve normal distributions show how continuous data is distributed and depict most of the data as concentrated on the mean or average in a normal distribution the area under the curve equals 1 and 68 27 of all data falls within 1 standard deviation how dispersed the numbers are from the mean 95 45 of all data falls within 2 standard deviations from the mean and approximately 99 73 of all data falls within 3 standard deviations from the mean 1 as the data points move away from the mean the frequency of data occurring decreases discrete uniform distribution shows that variables in a range have the same probability of occurring there are no variations in probable outcomes and the data is discrete rather than continuous its shape resembles a rectangle rather than the normal distribution s bell like a normal distribution however the area under the graph is equal to 1 