Condé Nast Traveler magazine conducts an annual survey of...

Condé Nast Traveler magazine conducts an annual survey of subscribers in order to determine the best places to stay throughout the world. Table 1.6 shows a sample of nine European hotels (Condé Nast Traveler, January 2000 ). The price of a standard double room during the hotel's high season ranges from $\$$ (lowest price) to $\$ \$ \$ \$$ (highest price). The overall score includes subscribers' evaluations of each hotel's rooms, service, restaurants, location/atmosphere, and public areas; a higher overall score corresponds to a higher level of satisfaction. a. How many elements are in this data set? b. How many variables are in this data set? c. Which variables are qualitative and which variables are quantitative? d. What type of measurement scale is used for each of the variables?

Condé Nast Traveler magazine conducts an annual survey of subscribers in order to determine the best places to stay throughout the world. Table 1.6 shows a sample of nine European hotels (Condé Nast Traveler, January 2000 ). The price of a standard double room during the hotel's high season ranges from $\$$ (lowest price) to $\$ \$ \$ \$$ (highest price). The overall score includes subscribers' evaluations of each hotel's rooms, service, restaurants, location/atmosphere, and public areas; a higher overall score corresponds to a higher level of satisfaction.
a. How many elements are in this data set?
b. How many variables are in this data set?
c. Which variables are qualitative and which variables are quantitative?
d. What type of measurement scale is used for each of the variables?

Key Concepts

Observational Units

Observational units are the individual items or entities that data is collected about in a study. Each unit is a single entity from the population under investigation, and the sample consists of all the units that have been observed or measured.

Variables

Variables are the characteristics or properties measured on each observational unit. They capture various aspects, traits, or features and can differ among the units in the study.

Qualitative and Quantitative Variables

Variables can be classified into qualitative (categorical) and quantitative. Qualitative variables describe attributes or categories that do not have a numerical value, while quantitative variables represent numerical measurements that indicate amounts or quantities.

Levels of Measurement

Levels of measurement describe the nature and precision of the data collected for each variable. Common scales include nominal (classification without a natural order), ordinal (categorical with a defined order), interval (numeric data with equal intervals but without a true zero), and ratio (numeric data with equal intervals and a meaningful zero), each of which guides the analysis techniques that can be applied.

Transcript

00:01 So in this question, there are three concepts we're going to be going over.

00:05 These are elements, variables, and measurement scales.

00:10 So we know that an element is simply an object in the set.

00:13 We know that variables are just characteristics of interest for these elements, and that they can be either qualitative or quantitative.

00:22 We know that if they're qualitative, they're going to be more focused on opinions and experiences, and they're also going to be more categorical.

00:29 Whereas if we're dealing with quantitative variables, they're just going to be concerned with numerical data.

00:36 And finally, we're dealing with our scales of measurement, and we have four that we're going to be dealing with.

00:42 So the first is the nominal scale, which just differentiates items based on the categories that they belong to.

00:48 Then we have our ordinal scale, which is basically the same as the nominal, except this time the order of these categories matters.

00:55 So it's more of a ranking system.

00:58 We also have our interval scale, and these are just ordered categories with equal intervals, and this scaling itself can go below, sorry, can go below zero.

01:09 And finally, we have a ratio scale, where we have ordered categories with equal intervals, and this scaling cannot go below zero.

01:19 So in this question, we're told that they call nastravel magazine, surveys at subscribers annually to determine the best places to stay throughout the world, and we have the data right here.

01:30 So in part a, we are asked to find out how many elements are in the set, and since we know that elements are just all the objects in our sample in this case, we know that since we're getting information on about 1, 2, 3, 4, 5, 6, 7, 8, 9 hotels, or 9 properties, that we have 9 elements in this set.

01:54 In part b, they're asking us to find the number of variables in this dataset.

01:59 Since we know that our variables are just characteristics of interest in our elements, they're what we're going to be trying to get information on through our set.

02:07 Survey.

02:08 So we can see that these variables are just country, room rate, number of rooms, and overall score.

02:19 So that means that there are four variables.

02:34 In part c, we're asked to determine which of our variables are quantitative and which are qualitative.

02:40 So if we're going to go through them in order, we first have country.

02:48 And since we can kind of use our country to kind of sort different properties, so for example, if we have two of them in england, we can put them in the england category, we can see that these are going to be more qualitative variables.

03:07 Now we're dealing with the concept of room rate...

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