D1. Data Basics

Question 1

Properties of categorical data

Answer 1

Qualitative: often represented using binary indicators (e.g. 1=employed, 0=unemployed).

Ordinal: order is meaningful but differences/ratios are not (e.g. 0=poor, 1=fair, 2=good).

Question 2

Properties of numerical data

Answer 2

Value is cardinally meaningful.

Discrete: number of individuals in the household.

Continuous: height, age, etc. Many variables in reality are treated as continuous even if they are discrete (quantity, wage).

Question 3

Define support

Answer 3

The set of values which a variable can take.

Discrete: usually an integer

Continuous: any real number (often within an interval).

Question 4

What is multivariate data?

Answer 4

Measuring multiple variables at once: multivariate variables (e.g. height, eye colour, weight or 2017, 2018, 2019).

Question 5

What is cross-sectional data?

Answer 5

Data on one attribute measured in N cases (e.g. people).

{X₁, X₂, …, X_N} = {X_i}_{i = 1, 2, …, N}

^ We ‘lay them out’ up and down on a real number line

If two attributes are measured, 2D number line.

If three, 3D number line.

Question 6

What is time-series data?

Answer 6

Series of data points indexed in time order.

{X₁, X₂, …, X_T} = {X_t}_{t = 1, 2, …, T}

Time is an implicit second attribute

Series is a sequence of bivariate observations {time, value}

Question 7

What sigma notations do we use for addition and multiplication?

Answer 7

Σ = add, Π = multiply