Indicate whether the following variables are categorical or numerical? If they are numerical, state whether they are discrete or continuous. (a) The price of randomly selected sweaters in a department store. (b) The first three digits of the social security number of randomly selected US residents. The eye color of randomly selected Columbia students. (c) The number of views of randomly selected YouTube videos. The speed of randomly selected cars on Broadway.

Question
Analyzing categorical data
asked 2021-02-08
Indicate whether the following variables are categorical or numerical? If they are numerical, state whether they are discrete or continuous.
(a) The price of randomly selected sweaters in a department store.
(b) The first three digits of the social security number of randomly selected US residents. The eye color of randomly selected Columbia students.
(c) The number of views of randomly selected YouTube videos. The speed of randomly selected cars on Broadway.

Answers (1)

2021-02-09
Step 1
Numerical data are also known as quantitative data that can be expressed in terms of numbers, whether discrete or continuous. Discrete data take integral values that are countable finite or infinite. Continuous data takes all numerical value on a number line viz. fractions or decimals. Examples of discrete data are Nuber of students, in a class, no of sands in a beach. Example of continuous data is weight and heights of school-going students. Level of measurement for numerical data is usually interval or ratio.
Categorical data are also known as qualitative data. They display qualitative characteristics like beauty, honesty, hence also known as attribute data. The level of measurement for categorical data is nominal or ordinal as they can either be named or ranked in terms of a particular order of preference.
Step 2
(a) The price of randomly selected sweaters in a department store are numerical Data. Since each sweater can be counted as a definite non-negative integral value, hence it is a discrete numerical variable.
(b) The first three digits of the social security numbers are categorical variable. This is because, although they consist of numbers they are used for identification of peoples and not for any algebraic treatment.
The eye colour of randomly selected Columbian students is a categorical variable. This is because qualitative or categorical variables—such as gender, hair colour, or ethnicity are used to group individuals
(c) The number of views of randomly selected YouTube videos is a discrete numerical variable. This is because the number is countable whether finite or countably infinite.
The speed of randomly selected cars on Broadway is a continuous numerical variable. This because speed can take any value (like 120 mph, 120.1 mph,120.2 mph and so on) if it is measured with an appropriate and accurate gauge.
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