A random variable is said to be discrete if the total number of values it can take can be counted. Alternatively, we can say that a discrete random variable can take only a discrete countable value such as 1, 2, 3, 4, etc. For example, in case of the roll of a die, there could be only 6 outcomes.

## Are house prices continuous or discrete data?

This is an example of a discrete random variable. Each outcome should also have a positive probability. The probabilities of each of these outcomes are given below:. In contrast to discrete random variable, a random variable will be called continuous if it can take an infinite number of values between the possible values for the random variable.

Examples include measuring the height of a person, or the amount of rain fall that a city receives. The number of possible outcomes is infinite. In that case, what is the probability that the random variable X will get a certain value x? P x will be 0 because we are talking about the possibility of one outcome from an infinite number of outcomes. In finance, some variables such as price change of a stock, or the returns earned by an investor are considered to be continuous, even though they are actually discrete, because the number of possible outcomes is large, and the probability of each outcome is very small.

For example, the probability of an investor earning a return of exactly 8. The probability distribution of a continuous random variable is called probability density function. Your email address will not be published. Save my name, email, and website in this browser for the next time I comment.

This site uses Akismet to reduce spam. Learn how your comment data is processed. Skip to primary navigation Skip to main content Skip to primary sidebar Skip to footer. Discrete Random Variable A random variable is said to be discrete if the total number of values it can take can be counted. The probabilities of each of these outcomes are given below: xi P xi 1 0. Note: What would be the probability of the random variable X being equal to 5?

Continuous Random Variable In contrast to discrete random variable, a random variable will be called continuous if it can take an infinite number of values between the possible values for the random variable. Leave a Reply Cancel reply Your email address will not be published.A clear understanding of the difference between discrete and continuous data is critical to the success of any Six Sigma practitioner.

The decision about which statistical test is appropriate under a specific set of circumstances very often depends on whether the underlying data is discrete or continuous. Discrete data are also referred to as attribute data. Discrete data take on a finite number of pre-determined points. The values that discrete data can take on are restricted to a list of two or more possibilities. Discrete data may be binary, where the value fits into one of two categories. For example, the sex of a person can take on two predetermined values — male or female.

A product may be defective or not defective. Discrete data may be ordinal, where values fit into one of three or more categories and there is an order or rank to the values. Finally, discrete data may be nominal where the data fit into one of three or more categories where the order of the categories is arbitrary.

For example, the color of a new car might fall into one of five categories — red, blue, silver, white and black. It should be noted that count data is discrete data. Items are counted in discrete units — one unit, two units, three units, etc.

For example, the number of correct answers on a 25 question test could be one of 26 values ranging from zero to Continuous data are also referred to as variable data. Continuous data exist on an interval and can take on any value. The number of possibilities for a continuous measurement within an interval is infinite.

Therefore, continuous data are measured on an infinitely divisible continuum. Examples of continuous data are the Ph of a solution, the length of an item in inches, and the weight of an item in pounds. A good rule of thumb is that if the unit of measure can be divided in half and still make sense, the data is continuous. A special case, and one which often confuses Six Sigma students, is percentage data. Technically speaking, percentage data is discrete because the underlying data that the percentages are calculated from is discrete.

For example, the percentage of defects is calculated by dividing the number of defects discrete count data by the total number of opportunities to have a defect discrete count data. In addition, dividing a percentage point into two or more parts still makes sense. Discrete data are easy to collect and interpret.

In Six Sigma we often talk about the number of defects, or the number of defects per million opportunities DPMO which are both discrete data.

The downside of discrete data is the loss of precision in measurement and the need for a larger amount of data to uncover patterns.

Continuous data give a greater sense of the variation that is present. For example, consider someone who has been determined to have been speeding on a highway where the speed limit is 65 miles per hour.

If we use discrete data, we only know whether someone was speeding over the speed limit of 65 mph or not speeding at or under the speed limit of 65 mph. If we collect continuous data we have more information to work with. For example, knowing that someone was traveling 68 miles per hour gives us a different understanding of their speed than knowing that they were traveling 95 miles per hour, even though both would be classified as speeding using discrete data.

In practice it is recommended to collect continuous data whenever possible and practical, and then convert it to discrete as required using a threshold value. In the case of highway speed, we would collect continuous data how fast the automobile was traveling in miles per hour and then determine whether the result is speeding or not speeding by comparing the actual speed to the threshold value of 65 miles per hour the speed limit.

Stm32 robot armYour comments or questions about this article are welcome, as are suggestions for future articles. Feel free to contact me by email at roger keyperformance. Roger C.

Bollette e prescrizione oltre 2 anni, finalmente si cambiaEllis is an industrial engineer by training and profession. He is a Six Sigma Master Black Belt with over 45 years of business experience in a wide range of fields. For a more detailed biography, please refer to www.Receive emails about upcoming NOVA programs and related content, as well as featured reporting about current events through a science lens.

Split a mile in half, you get half a mile. Can this slicing continue indefinitely, or will you eventually reach a limit: a smallest hatch mark on the universal ruler? The success of some contemporary theories of quantum gravity may hinge on the answer to this question.

But the puzzle goes back at least years, to the paradoxes thought up by the Greek philosopher Zeno of Elea, which remained mysterious from the 5th century BC until the early s.

Foscam r4 rtspThe tortoise gets a head start on the faster-running Achilles. While Achilles pursues the tortoise to cover this additional distance, the tortoise moves yet another bit. Obviously, in real life, Achilles wins the race. So, Zeno argued, the assumptions underlying the scenario must be wrong. Specifically, Zeno believed that space is not indefinitely divisible but has a smallest possible unit of length. This allows Achilles to make a final step surpassing the distance to the tortoise, thereby resolving the paradox.

After mathematicians understood how to sum an infinite number of progressively smaller steps, they calculated the exact moment Achilles surpasses the tortoise, proving that it does not take forever, even if space is indefinitely divisible. In this case, the infinities were not mistakes but demonstrably a consequence of applying the rules of quantum theory to gravity.

But by positing a smallest unit of length, just like Zeno did, theorists can reduce the infinities to manageable finite numbers. And one way to get a finite length is to chop up space and time into chunks, thereby making it discrete: Zeno would be pleased. He would also be confused. Think of studying samples with a microscope, for example. Magnify too much, and you encounter a resolution-limit beyond which images remain blurry. And if you zoom into a digital photo, you eventually see single pixels: further zooming will not reveal any more detail.

In both cases there is a limit to resolution, but only in the latter case is it due to discretization. In these examples the limits could be overcome with better imaging technology; they are not fundamental. But a resolution-limit due to quantum behavior of space-time would be fundamental. It could not be overcome with better technology. So, a resolution-limit seems necessary to avoid the problem with infinities in the development of quantum gravity.

But does space-time remain smooth and continuous even on the shortest distance scales, or does it become coarse and grainy? Researchers cannot agree. In string theory, for example, resolution is limited by the extension of the strings roughly speaking, the size of the ball that you could fit the string insidenot because there is anything discrete. In a competing theory called loop quantum gravity, on the other hand, space and time are broken into discrete blocks, which gives rise to a smallest possible length expressed in units of the Planck length, about 10 metersarea and volume of space-time—the fundamental building blocks of our universe.

Einstein taught us that space and time are joined in one entity: space-time. But some dissidents argue that only space or only time should be discrete. So how can physicists find out whether space-time is discrete or continuous? Directly measuring the discrete structure is impossible because it is too tiny. But according to some models, the discreteness should affect how particles move through space.

Menu module in oracle formsIt is a miniscule effect, but it adds up for particles that travel over very long distances. If true, this would distort images from far-away stellar objects, either by smearing out the image or by tearing apart the arrival times of particles that were emitted simultaneously and would otherwise arrive on Earth simultaneously.

Even if the direct effects on particle motion are unmeasurable, defects in the discrete structure could still be observable. Think of space-time like a diamond.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up.

Discrete data can only take particular values. There may potentially be an infinite number of those values, but each is distinct and there's no grey area in between. Discrete data can be numeric -- like numbers of apples -- but it can also be categorical -- like red or blue, or male or female, or good or bad.

Continuous data are not restricted to defined separate values, but can occupy any value over a continuous range. Between any two continuous data values, there may be an infinite number of others. Continuous data are always essentially numeric. It sometimes makes sense to treat discrete data as continuous and the other way around :. For example, something like height is continuous, but often we don't really care too much about tiny differences and instead group heights into a number of discrete bins -- i.

Conversely, if we're counting large amounts of some discrete entity -- i. It can also sometimes be useful to treat numeric data as categoricaleg: underweight, normal, obese. This is usually just another kind of binning.

Data is always discrete. Given a sample of n values on a variable, the maximum number of distinct values the variable can take is equal to n. See this quote. All actual sample spaces are discrete, and all observable random variables have discrete distributions. The continuous distribution is a mathematical construction, suitable for mathematical treatment, but not practically observable.

Pitmanp.A continuous random variable can take all values in an interval, while discrete variable can only take countable values. The variable "cost" is always rounded to 2 decimal places, and that's why it cannot take all possible values in an interval, so this technically should be discrete.

But if you measure it accurately it should be treated as continuous. Also refer to this answer by George. Is the cost of a loaf of bread discrete or continuous? Feb 13, Explanation: A continuous random variable can take all values in an interval, while discrete variable can only take countable values.

Related questions What are Box-and-Whisker Plots? What is the importance of descriptive statistics? What is the difference between a population and a sample? Why do statisticians use samples? What are some benefits of using a sample instead of a census? What is the difference between continuous data and discrete data? Give an example of each: continuous data and discrete data. Which of the following would be classified as categorical data?

## Discrete Vs. Continuous Random Variable

How do you determine whether the quantitative variable is discrete or continuous given the See all questions in What is Statistics? Impact of this question views around the world. You can reuse this answer Creative Commons License.Variable refers to the quantity that changes its value, which can be measured. It is of two types, i. The former refers to the one that has a certain number of values, while the latter implies the one that can take any value between a given range.

Data can be understood as the quantitative information about a specific characteristic. The characteristic can be qualitative or quantitative, but for the purpose of statistical analysis, the qualitative characteristic is transformed into quantitative one, by providing numerical data of that characteristic.

So, the quantitative characteristic is known as a variable.

Se12 londonHere in this article, we are going to talk about the discrete and continuous variable. Basis for Comparison Discrete Variable Continuous Variable Meaning Discrete variable refers to the variable that assumes a finite number of isolated values. Continuous variable alludes to the a variable which assumes infinite number of different values. Range of specified number Complete Incomplete Values Values are obtained by counting.

Values are obtained by measuring. Classification Non-overlapping Overlapping Assumes Distinct or separate values. Any value between the two values. Represented by Isolated points Connected points. A discrete variable is a type of statistical variable that can assume only fixed number of distinct values and lacks an inherent order. Also known as a categorical variablebecause it has separate, invisible categories.

However no values can exist in-between two categories, i. So, the number of permitted values that it can suppose is either finite or countably infinite.

Hence if you are able to count the set of items, then the variable is said to be discrete. Continuous variable, as the name suggest is a random variable that assumes all the possible values in a continuum. Simply put, it can take any value within the given range.

### Are Space and Time Discrete or Continuous?

So, if a variable can take an infinite and uncountable set of values, then the variable is referred as a continuous variable. A continuous variable is one that is defined over an interval of values, meaning that it can suppose any values in between the minimum and maximum value.

It can be understood as the function for the interval and for each function, the range for the variable may vary.If you have a discrete variable and you want to include it in a Regression or ANOVA model, you can decide whether to treat it as a continuous predictor covariate or categorical predictor factor.

If the discrete variable has many levels, then it may be best to treat it as a continuous variable. Treating a predictor as a continuous variable implies that a simple linear or polynomial function can adequately describe the relationship between the response and the predictor. When you treat a predictor as a categorical variable, a distinct response value is fit to each level of the variable without regard to the order of the predictor levels.

Use this information, in addition to the purpose of your analysis to decide what is best for your situation. What are categorical, discrete, and continuous variables? Learn more about Minitab. Quantitative variables can be classified as discrete or continuous. Categorical variable Categorical variables contain a finite number of categories or distinct groups. Categorical data might not have a logical order.

For example, categorical predictors include gender, material type, and payment method. Discrete variable Discrete variables are numeric variables that have a countable number of values between any two values.

A discrete variable is always numeric. For example, the number of customer complaints or the number of flaws or defects. Continuous variable Continuous variables are numeric variables that have an infinite number of values between any two values. For example, the length of a part or the date and time a payment is received. By using this site you agree to the use of cookies for analytics and personalized content. Read our policy.

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