Table 1.7 shows data for seven colleges and universities. The endowment fin billions of dollars)

Table 1.7 shows data for seven colleges and universities....

Key Concepts

Data Element

A data element, often simply called an element, refers to a single unit of information collected in a dataset. In the context of a dataset where each row represents a distinct college or university, each element would be an individual college or university entry.

Variable

A variable is a characteristic or attribute that can take on different values across the data elements. In a dataset, each column represents a variable that describes some aspect of the elements, such as an institution's endowment size or location.

Quantitative Variable

A quantitative variable is a variable that can be measured numerically and where arithmetic operations, such as calculating means or differences, make sense. In the dataset, examples include numerical values like the endowment size (in billions of dollars) and the acceptance rate (percentage of applicants admitted).

Categorical Variable

A categorical variable describes attributes that can be divided into distinct groups or categories that do not have a natural numeric order. Examples from the dataset include the state the school is located in, the campus setting, and the NCAA Division for varsity teams, which classify the data into various groups without inherent quantitative meaning.

Transcript

00:01 Hey everyone, today we're answering problem number four from chapter one of the principles of modern business statistics textbook.

00:11 In this problem, there are three parts.

00:14 In part a, we are asked to find how many elements there are in the dataset.

00:18 In part b, we are asked to find how many variables there are in the data set.

00:23 And then in part c, we're asked to classify those x amount of variables into either categorical variables or, quantitative variables.

00:33 So let's start off with part a.

00:35 How many elements are there? the data set are defined as the things that data are being collected on.

00:46 So what are we collecting data on? well, clearly, we're collecting data on these schools.

00:54 So amherst, duke, harvard, swarthmore, uk, williams, and yale.

00:58 So i see how many? one, two, three, four, five, six, seven.

01:02 So i see seven colleges slash university.

01:04 So there's.

01:05 They're going to be seven.

01:08 Also, an easy way to see this is that you actually can just look at the title and they tell you data for seven colleges and universities.

01:14 So there are seven elements.

01:16 All right, moving on to part b, where we are asked to find how many variables there are.

01:21 So variables are characteristics of interest about the elements.

01:26 So what are we interested in finding out about these colleges and universities? we're interested in finding out what state they're in.

01:34 Number one, number two, their campus studying type, number three, their endowment in billions of dollars, number four, the percentage of their applicants that were admitted, and number five, their ncaa division.

01:47 So there are clearly five points of interest for characteristics of interest regarding the elements, which in this case are the colleges and universities.

01:57 All right, so part a, the answer is seven, part b, the answer is five.

02:02 Now part c.

02:03 We know that there has to be five variables.

02:06 We have to classify those into categorical or quantitative.

02:09 Categorical variables tend to deal with things that are not numeric, well, they could be either numerical or non -numerical, but categorical variables deal with things that are labeled or name, and typically don't have numbers more often than not.

02:26 But sometimes they do.

02:28 So let's see.

02:29 So state where the location is for this, that is a category.

02:34 Because we see that two of the seven are in the category of massachusetts, actually three of the seven.

02:41 Two of the seven are in pennsylvania.

02:43 One of the seven is in north carolina and one of the seven is in connecticut.

02:46 So state location is going to be categorical.

02:50 And quantitative while i'm running categorical variables, i'm listing them.

02:56 Quantitative variables are defined as numerical values that determine something about your element.

03:04 As we'll see very soon.

03:07 So campus setting.

03:08 Okay, well, i have different categories.

03:12 Clearly, i have city, mid -sized, city, mid -sized, town, fringe, city -large, and suburb large.

03:18 So i see four different categories that classify my campus setting...

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