Continuous and Discrete Data
Continuous data can take on any value within a given range and can be measured. It includes values such as height, weight, and temperature. Discrete data, on the other hand, consists of distinct, separate values and is typically counted. Examples include the number of students in a class or the number of cars in a parking lot.
7 Key excerpts on "Continuous and Discrete Data"
eBook - ePubStatistics: An Introduction: Teach Yourself
The Easy Way to Learn Stats
- Alan Graham(Author)
- 2017(Publication Date)
- Teach Yourself(Publisher)
...4 Choosing a suitable graph In this chapter you will learn: • how to distinguish between two important types of data (discrete and continuous) • the difference between single and paired data • common types of statistical judgement (summarizing, comparing and inter-relating) • how to choose the right graph for your needs. In the previous chapter, a variety of different types of graph were merely described, without any real explanation of when and how they might be used. We now turn to this question of deciding which graph is most suitable for which situation. Essentially, two key factors help you to determine which is the best graph to draw. These are the type of data being represented and the type of statistical judgement which you hope the graph will help you to make. These two aspects are discussed in the first two sections below. In the final section of the chapter, examples will be provided to give you practice at choosing the best graph to represent your data, guided by the principles of the first two sections. Types of data Statisticians have come up with a variety of sophisticated and elegant ways of classifying data according to a variety of different attributes. However, since the whole point of this section is to help you decide which graph to choose, we will restrict attention to a simple way of classifying data which informs the choice of graph. DISCRETE AND CONTINUOUS DATA The most basic distinction that can be made between types of data is to separate those that are discrete from those that are continuous. A dictionary definition of the word discrete will read something like ‘separate, detached from others, individually distinct, discontinuous’. Table 4.1 shows a few examples of discrete data. Nugget: discrete, discreet Don’t confuse the words discrete and discreet ; they sound the same but have quite different meanings...
eBook - ePubChoosing and Using Statistics
A Biologist's Guide
- Calvin Dytham(Author)
- 2011(Publication Date)
- Wiley-Blackwell(Publisher)
...They can be further subdivided. Continuous variables This type of variable (sometimes called ‘interval’ variables) theoretically has an infinite number of values between any two points. Of course in practice the accuracy of measurement will not be perfect, as it will be limited by the observer and the equipment used. Therefore there will only be a limited number of possible values between any two points. Obvious examples of continuous variables are lengths, weights and areas. Note: accuracy and precision are two words that are often confused. Accuracy is the closeness to the real value. This is usually set by the observer or the equipment and should be chosen as appropriate to the variable. When you write down a value it should reflect the accuracy with which the measurement was taken. If you measure to the nearest 0.1 g then 5 g should be written as 5.0 g, not 5.00 g; Precision is the closeness of repeated measures to the same value. It is possible to have data that are very precise but very inaccurate. For example, your balance gives exactly the same value for repeated measures of the same object but they are all overweight because the balance was not calibrated properly. The data obtained would be precise but inaccurate. Discrete variables Unlike continuous variables this type of variable (also called ‘discontinuous’ or occasionally ‘meristic’) has a limited number of possible values. These possibilities are often, but not always, integers. For example, number of live-born offspring in a litter of mice can only ever be an integer as there is no possibility of recording a fraction of an offspring. Discrete variables are often produced by questionnaires. Respondents are offered choices such as: 1, strongly disagree; 2, slightly disagree; 3, neutral; 4, slightly agree; 5, strongly agree. There is clearly a continuous variable (‘agreement’) here and division of responses into categories in this way is rather arbitrary...
eBook - ePub- Perumal Mariappan(Author)
- 2019(Publication Date)
- Chapman and Hall/CRC(Publisher)
...Both should convey the meaning of the content of the table. • Each table should bear a table number. The number can be like 1, 2, and so on or double-numbered, such as 1.1, 1.2. The first kind of numbers conveys the sequence of the table. The second kind of numbers conveys the sequence and which chapter or part of the material the table can be found. • The use of the contents should be clearly mentioned (e.g., instead of a head, sales, it can be, sales in rupees). • As far as possible, the length and breadth of the table must be evenly spaced. • At times, it can be adjusted based on the lengthy columns. • The columns to be compared must be placed in succession. • The total values of columns must be placed at the bottom of the table. • The source of the data should be mentioned at the end of the table. 3.4 Types of Variables and Data Variables can be classified into two types. They are discrete and continuous variables. Discrete Variable A variable that can take only isolated or discrete value is called a ‘discrete variable’. Example : X refers to the age of 5 members. Continuous Variable A variable that assumes any real value (i.e., integer/fraction) within a specified limit is called a ‘continuous variable’. Example : X refers to the range of marks secured by students. Discrete Data The values taken by the discrete variable is called ‘discrete data’. Continuous Data The values taken by the continuous variable is called ‘continuous data’. 3.5 Levels of Measurement In statistics, measurement is the assignment of numbers to attributes of objects or observations. The level of measurement is a function of the rules used to assign numbers and is an important aspect in determining what type of statistical analysis can be approximately applied to the data. 3.5.1 Nominal Scale The lowest or weakest level of measurement is the use of numbers to classify observations into mutually exclusive classes or groups...
eBook - ePub- Rafael Perera, Carl Heneghan, Douglas Badenoch(Authors)
- 2011(Publication Date)
- BMJ Books(Publisher)
...Data: describing and displaying The type of data we collect determines the methods we use. When we conduct research, data usually comes in two forms: Categorical data, which give us percentages or proportions (e.g. ‘60% of patients suffered a relapse’). Numerical data, which give us averages or means (e.g. ‘the average age of participants was 57 years’). So, the type of data we record influences what we can say, and how we work it out. This section looks at the different types of data collected and what they mean. Any measurable factor, characteristic or attribute is a variable A variable from our data can be two types: categorical or numerical. Categorical: the variables studied are grouped into categories based on qualitative traits of the data. Thus the data are labelled or sorted into categories. A special kind of categorical variables are binary or dichotomous variables: a variable with only two possible values (zero and one) or categories (yes or no, present or absent, etc.; e.g. death, occurrence of myocardial infarction, whether or not symptoms have improved). Numerical: the variables studied take some numerical value based on quantitative traits of the data. Thus the data are sets of numbers. You can consider discrete as basically counts and continuous as measurements of your data. Censored data – sometimes we come across data that can only be measured for certain values: for instance, troponin levels in myocardial infarction may only be detected for a certain level and below a fixed upper limit (0.2-180 μg/L) Summarizing your data It’s impossible to look at all the raw data and instantly understand it. If you’re going to interpret what your data are telling you, and communicate it to others, you will need to summarize your data in a meaningful way...
- David Lucy(Author)
- 2013(Publication Date)
- Wiley(Publisher)
...2 Data types, location and dispersion All numeric data can be classified into one or more types. For most types of data the most basic descriptive statistics are a measure of central tendency, called location, and some measure of dispersion, which to some extent is a measure of how good is a description the measure of central tendency. The concepts of location and dispersion do not apply to all data types. 2.1 Types of data There are three fundamental types of data: 1. Nominal data are simply classified into discrete categories, the ordering having no significance. Biological sex usually comes in male/female, whereas gender can be male/female/other. Things such as drugs can be classified by geographical area such as South American, Afghan, Northern Indian or Oriental. Further descriptions by some measure of location, and dispersion, are not really relevant to data of this type. 2. Ordinal data are again classified into discrete categories; this time the ordering does have significance. The development of the third molar (Solari and Abramovitch, 2002) was classified into 10 stages. Each class related to age, and therefore the order in which the classes appear is important. 3. Continuous data types can take on any value in an allowed range. The concentration of magnesium in glass is a continuous data type which can range from 0% to about 5% before the glass becomes a substance which is not glass. Within that range magnesium can adopt any value such as 1.225% or 0.856%. Table 2.1 Table of year and Δ 9 -THC (%) for marijuana seizures: these data are simulated (with permission) from ElSohly et al. (2001) and are more fully listed in Table 2.2 Table 2.2 Table of year and Δ 9 -THC (%) for marijuana seizures: these data are simulated (with permission) from ElSohly et al. (2001) The type of data sometimes restricts the approaches which can be used to examine and make inferences about those data...
eBook - ePubStatistics
The Essentials for Research
- Henry E. Klugh(Author)
- 2013(Publication Date)
- Psychology Press(Publisher)
...Family size, number of parking tickets, and number of siblings are discrete variables. Unfortunately this distinction can become a bit blurred when we apply it to achievement test scores. If a test has 50 items, it would appear that we have a discrete variable; you can get 39 right or 40 right but not 39.126 right. However, we usually treat test scores as if they were continuous variables. We assume that instead of measuring achievement with a 50-item test we could have used a 500-item test or a 5000-item test so that we could, in theory, have an infinitely dividable continuous scale. We will say more about this issue a bit later. 2.4 Frequency Distributions Regardless of the scale of measurement used, the data from an experiment must be presented in an orderly fashion. Suppose we wish to compare the effectiveness of two different methods of instruction. We may have test scores from one group of students taught by the lecture method and another group taught by the discussion method, and we may wish to compare the two sets of scores. The data may be compared more easily if we first tabulate the scores into two frequency distributions. A frequency distribution is a listing of all the different score values in order of magnitude with a tally or count of the number of scores at each value. Table 2.2 shows two frequency distributions that might result if our data were presented in this form. Table 2.2 Frequency Distributions of Examination Scores for Students Taught by Lecture and by Discussion Methods With the scores pictured as they are in Table 2.2 we can see some differences between the distributions. The lecture method seems to produce higher achievement, but the range of scores is about the same. We can also observe that the scores of the lecture students tend to be concentrated toward the top of the distribution, while the scores of the discussion group seem to be more symmetrically distributed about a central value...
eBook - ePubIntroductory Probability and Statistics
Applications for Forestry and Natural Sciences (Revised Edition)
- Robert Kozak, Antal Kozak, Christina Staudhammer, Susan Watts(Authors)
- 2019(Publication Date)
- CAB International(Publisher)
...A discrete sample space is one that contains a finite number of elements, such as the eight possible outcomes from tossing a coin three times. A discrete sample space can also be unending, but countable, such as the sample space associated with tossing a coin until a head appears (the number of tosses necessary to meet this condition is the set of all possible whole numbers). Discrete random variables always take the form of data that are counted, such as the number of infested trees or the number of accidents per month in a logging camp. A continuous sample space is one that contains an infinite and uncountable number of outcomes. Any random variable obtained by measurements, like the time to germination, the weight of salmon, the distance between forest dependent com muni ties, or the volume of a tree, can theoretically take on any value in a measurement interval. For instance, for any two given merchantable tree volumes, e.g. 3.1 m 3 and 3.2 m 3, one can always find another value that occurs between them (e.g. 3.17 m 3). Theoretically, this could go on infinitely if measurement instruments were precise enough. Random variables defined over discrete sample spaces are called discrete random variables, while random variables defined over continuous sample spaces are called continuous random variables. 4.2 Probability Distributions A discrete random variable can be described by the probabilities that each of its individual values takes on when the random experiment is carried out. The list of all possible numerical outcomes and their associated probabilities is called the probability distribution of the random variable...
