Which of the following quantities are discrete?
http://www.merriam-webster.com/dictionar... definition: "2 a: consisting of distinct or unconnected elements : noncontinuous b: taking on or having a finite or countably infinite number of values
What type of data consists of all possible values along a number line for a specified interval?
Quantitative data can be either discrete or continuous. Discrete data are data that can be listed or placed in order. Usually, but not always, there is a finite quantity of discrete data (e.g., a list of the possible outcomes of an activity such as rolling a die). However, discrete data can be "countably" infinite. For example, suppose , where n = 1, 2, 3,… Then the first outcome corresponds to n = 1, the second to n = 2, etc. There is an infinite number of outcomes, but they are countable (you can identify the first term, the second, etc., but there is no last term).Continuous data can be measured, or take on values in an interval. The number of heads we get on 20 flips of a coin is discrete; the time of day is continuous. We will see more about discrete and continuous data later on. http://www.education.com/study-help/article/quantitative-qualitative-data/ As you can see, it applies the same, as the values along a number line for a specified interval are "countably&q
How does quantitative reasoning differ from qualitative reasoning?
Qualitative is very closely linked to logic of existence - is it there or is it not there?Quantitative is more a question of how much (of it), how often, to which degree.The two merge in those cases where a quality has been defined, allowing it to be counted/measured (not just identified).An example of this is "sentiment" - once it has been operationalized how sentiment is to be operationally recognized it becomes posssible to express insights about sentiment that include quantitative results:This example shows the sentiment of President Trump's first address before a joint Meeting of Congress:The lines illustrate presense of expressions that are of a feeling-up and a feeling-down nature. We see the President starting predominantly in the positive and ending in the same way. Three-quarters into the speech he moves up the “difficult” stuff and the lines get to touch. But the finishing-off is positive.We can make these kinds of reasoning because a tool was built that takes into consideration the qualitative aspect of your topic - allowing us to quantify their presense.
What is the difference between a discrete variable and continuous variable?
A discrete variable is that which takes values obtained by counting. For example: the number of sides of a coin, the number of sides of a dice, number of pieces in chess, number of words in a book, and the number of players in a team are all discrete.My way of explaining a discrete variable is that it takes values whose half may or may not make sense. For example, half a dozen eggs is [math]6[/math], and the half of [math]6[/math] eggs is [math]3[/math], both make sense, but the half of [math]3[/math] makes no sense hence one cannot equally distribute [math]3[/math] eggs to [math]2[/math] people.A continuous variable is that which takes values obtained by measuring. For example: the height of a person is continuous since it is measured.My way of explaining a continuous variable is that it takes values whose half always makes sense. For example, half a height of a person can be the height of another person or something else.Given a variable [math]v[/math] such that [math]v \in (a,b)[/math] where [math]a[/math] and [math]b[/math] are integers. If [math]v[/math] is discrete, then [math](a,b)[/math] is always a finite set of numbers, else if [math]v[/math] is continuous, then [math](a,b)[/math] is always a infinite set of numbers. For example, there are seven discrete numbers in [math](0,9)[/math] but infinitely many continuous numbers.A discrete variable takes integral values whereas continuous variable takes any real (integral or rational or irrational) values.
What is the difference between continuous and discrete data?
This question can lead to ambiguous answers, which can be resolved by understanding the context of application.Let’s look at time series data with real-world examples where the time and value of each data point has significance:there’s discrete-time continuous valued data (e.g, daily average temperature), andthere is discrete-time discrete valued data (e.g., number of people travelling on train each month)continuous-time discrete valued data (e.g., number of people waiting to be seen at an ER over a period of time - modeled as Continuous time Markov process)continuous-time continuous-valued data (e.g. speed of a car as it traverses a path for a given interval of time)In another context all data is classified as either categorical or quantitative based solely on the value.Categorical data doesn’t have a measure of value. That is, no metric of large/small or strong/weak is applicable to a dataset whose individual data are names or labels. Examples: names fruit {Mango, Orange, Kiwi, Pineapple}, colors of rainbow {R, O, Y, G, B, V}, two-way switch state {0, 1}, etc.Quantitative data does have a measure of value. There’s two subcategories in quantitative data which are discrete-valued and continuous-valued quantitative data. In this context 1. and 4. above would be continuous data, and 2. and 3. would be discrete data.Bottom line - context matters!
What is discrete mathematics and why is it so important for computer science?
Discrete mathematics - at least as I learned it - is a collection of techniques and algorithms relevant to all sorts of things you often need to do when programming:Working with graphs, i.e. collections of nodes and edges. How do you find the quickest way across town? How can you drive around a neighborhood to deliver papers, making sure you drive on each road exactly once? How much water can a complicated pipeline deliver to all the homes connected to it? What’s the bottleneck for fed-ex delivering packages all over the world? All of these can be solved with graph theory.Complexity theory: given three ways of solving a problem, which one will work faster? This is harder to figure out than it sounds.Problems where you need to classify objects and check for their membership: is it a type of duck? a dog? how many creatures are in each category? Set theory give you a way to work with this sort of question.There’s a lot more to it, but this is some of the highlights.I’ve taken a lot of computer science courses over the year. The single most useful was, without a doubt, discrete mathematics. It’s the only course with unintuitive content that was directly applicable to work in industry.Well, that and perhaps introduction to algorithms, and intro to programming.