Discrete vs continuous data are two broad categories of numeric variables. Numeric variables represent characteristics that you can express as numbers rather than descriptive language. Show
When you have a numeric variable, you need to determine whether it is discrete or continuous. In broad strokes, the critical factor is the following:
Let’s dig a little deeper into the differences! I’ll explain the differences and provide examples of discrete vs continuous data. Related post: What is a Variable? What is Discrete Data?Discrete variables can only assume specific values that you cannot subdivide. Typically, you count them, and the results are integers. For example, if you work at an animal shelter, you’ll count the number of cats. Discrete data can only take on specific values. For example, you might count 20 cats at the animal shelter. These variables cannot have fractional or decimal values. You can have 20 or 21 cats, but not 20.5! Natural numbers have discrete values. Other examples of discrete variables include the following:
While discrete data have no decimal places, the average of these values can be fractional. For example, families can have only a discrete number of children: 1, 2, 3, etc. However, the average number of children per family can be 2.2. Frequently, you’ll use bar charts to graph discrete data because the separate bars emphasize the distinct nature of each value. However, it’s appropriate to use other graphs as well.  When you have discrete values of a qualitative nature (i.e., attributes rather than numbers), it’s called categorical or nominal data. What is Continuous Data?Continuous variables can assume any numeric value and can be meaningfully split into smaller parts. Consequently, they have valid fractional and decimal values. In fact, continuous data have an infinite number of potential values between any two points. Generally, you measure them using a scale. When you see decimal places for individual values, you’re looking at a continuous variable. Examples of continuous data include weight, height, length, time, and temperature. Frequently, you’ll use histograms and scatterplots to graph continuous data. These graphs are designed to handle values that fall on a continuous spectrum and have decimal places.
Both types of variables are essential in statistics. At the animal shelter, after counting the cats, you’ll weigh them. The counts are discrete values while their weights are continuous. Chances are you’ll need to analyze both types of variables. It’s vital to recognize discrete vs continuous data because there are different ways to graph and analyze them. To learn more about how to assess different types of variables, read the following posts:
Discrete Random VariablesA discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,........ Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, the number of defective light bulbs in a box of ten.The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function. (Definitions taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1) Suppose a random variable X may take k different values, with the probability that X = xi defined to be P(X = xi) = pi. The probabilities pi must satisfy the following: 1: 0 < pi < 1 for each i 2: p1 + p2 + ... + pk = 1.ExampleThe probabilities associated with each outcome are described by the following table: Outcome 1 2 3 4 Probability 0.1 0.3 0.4 0.2The probability that X is equal to 2 or 3 is the sum of the two probabilities: P(X = 2 or X = 3) = P(X = 2) + P(X = 3) = 0.3 + 0.4 = 0.7. Similarly, the probability that X is greater than 1 is equal to 1 - P(X = 1) = 1 - 0.1 = 0.9, by the complement rule. This distribution may also be described by the probability histogram shown to the right: All random variables (discrete and continuous) have a cumulative distribution function. It is a function giving the probability that the random variable X is less than or equal to x, for every value x. For a discrete random variable, the cumulative distribution function is found by summing up the probabilities. (Definition taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1) ExampleThe probability that X is less than or equal to 1 is 0.1, the probability that X is less than or equal to 2 is 0.1+0.3 = 0.4, the probability that X is less than or equal to 3 is 0.1+0.3+0.4 = 0.8, and the probability that X is less than or equal to 4 is 0.1+0.3+0.4+0.2 = 1. The probability histogram for the
cumulative distribution of this random variable is shown to the right: Continuous Random VariablesA continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile.(Definition taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1) A continuous random variable is not defined at specific values. Instead, it is defined over an interval of values, and is represented by the area under a curve (in advanced mathematics, this is known as an integral). The probability of observing any single value is equal to 0, since the number of values which may be assumed by the random variable is infinite. Suppose a random variable X may take all values over an interval of real numbers. Then the probability that X is in the set of outcomes A, P(A), is defined to be the area above A and under a curve. The curve, which represents a function p(x), must satisfy the following: 1: The curve has no negative values (p(x) > 0 for all x) 2: The total area under the curve is equal to 1.A curve meeting these requirements is known as a density curve. The Uniform DistributionA random number generator acting over an interval of numbers (a,b) has a continuous distribution. Since any interval of numbers of equal width has an equal probability of being observed, the curve describing the distribution is a rectangle, with constant height across the interval and 0 height elsewhere. Since the area under the curve must be equal to 1, the length of the interval determines the height of the curve.The following graphs plot the density curves for random number generators over the intervals (4,5) (top left), (2,6) (top right), (5,5.5) (lower left), and (3,5) (lower right). The distributions corresponding to these curves are known as uniform distributions. P(X < 3 and X > 5) = P(X < 3) + P(X > 5) = (3-2)*0.25 + (6-5)*0.25 = 0.25 + 0.25 = 0.5. The uniform distribution is often used to simulate data. Suppose you would like to simulate data for 10 rolls of a regular 6-sided die. Using the MINITAB "RAND" command with the "UNIF" subcommand generates 10 numbers in the interval (0,6): MTB > RAND 10 c2; SUBC> unif 0 6.Assign the discrete random variable X to the values 1, 2, 3, 4, 5, or 6 as follows: if 0<X<1, X=1 if 1<X<2, X=2 if 2<X<3, X=3 if 3<X<4, X=4 if 4<X<5, X=5 if X>5, X=6. Use the generated MINITAB data to assign X to a value for each roll of the die: Uniform Data X Value 4.53786 5 5.77474 6 3.69518 4 1.03929 2 4.23835 5 0.37096 1 0.75272 1 5.56563 6 0.89045 1 3.18086 4 Another type of continuous density curve is the normal distribution. The area under the curve is not easy to calculate for a normal random variable X with mean What is a type of variable that can infinite number on the value that can occur within a population?A variable is said to be continuous if it can assume an infinite number of real values within a given interval.
Can infinite numbers have possible values?A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements.
What are the types of continuous variables?There are two types of continuous variables namely interval and ratio variables.
What is a random variable where the data can take infinitely many values?A continuous random variable is a random variable where the data can take infinitely many values. For example, a random variable measuring the time taken for something to be done is continuous since there are an infinite number of possible times that can be taken.
|
What is a type of variable that can take infinite number on the value that can occur within a population?
zusammenhängende Posts
Urheberrechte © © 2024 defrojeostern Inc.
