BUSN1018 Descriptive Statistics I

Flashcards covering the fundamentals of descriptive and inferential statistics, data types, levels of measurement, and sampling designs based on the BUSN1018 lecture notes.

Statistics

A branch of mathematics dealing with the analysis and interpretation of masses of data.

Variable

The characteristic of interest being measured, such as height, temperature, or gender.

Data

A set of values or observations for one or more variables used to evaluate performance, test theories, or estimate population characteristics.

Descriptive Statistics

Branch of statistics used to collect, describe, organize, and present data, often visually using tools like histograms or pie charts.

Inferential Statistics

Branch of statistics used to draw conclusions or make decisions about a larger population based only on sample data.

Population

The total set of all elements or observations of interest, denoted by the size $N$.

Census

A survey or measurement where the entire population is measured.

Sample

A subset of the population used to obtain information, denoted by the size $n$.

Parameter

A descriptive measure calculated from a population, typically represented by Greek letters like population mean ($\mu$) or population variance ($\sigma^2$).

Statistic

A descriptive measure calculated from a sample, typically represented by Roman letters like sample mean ($\bar{x}$) or sample variance ($s^2$).

Sampling Error

The difference between a characteristic's value in the population parameter and its value in a sample statistic ($\text{Sampling Error} = \text{Parameter} - \text{Statistic}$).

Primary Data

Data collected specifically for the purpose of the current analysis.

Secondary Data

Data collected for some other reason that is already available from print or electronic sources, such as government or industry records.

Qualitative/Categorical Data

Data formed into distinct groupings or categories that typically take a language value rather than a numerical one.

Quantitative/Numerical Data

Data that has a numerical value representing a measured or counted quantity.

Discrete Numerical Variable

A quantitative variable where possible values can be listed, often occurring as integer values such as $0, 1, 2, 3...$

Continuous Numerical Variable

A quantitative variable that is measurable and can have any real number value, including decimals, such as weight or temperature.

Nominal Level Data

The lowest level of measurement used only to classify or categorize different items, where numbers are only used as labels.

Ordinal Level Data

A level of measurement where numbers indicate rank or order, meaning the relative magnitude is significant, but differences between numbers are not comparable.

Interval Level Data

Numerical data where distances between consecutive integers have meaning, but zero is a matter of convenience rather than a fixed starting point (e.g., Celsius temperature).

Ratio Level Data

The highest level of measurement, containing all properties of interval data with the addition of a meaningful zero point representing the absence of the phenomenon.

Sampling Frame

A listing of the population from which a sample is chosen.

Non-sampling Errors

Errors in a survey that occur due to a faulty sampling frame, non-response, recording errors, or data processing errors.

Random (Probability) Sampling

A method where subjects are chosen from the population with a known probability, allowing for the application of probability theory to make inferences.

Simple Random Sample (SRS)

A sampling technique where every individual or item from the sampling frame has an equal chance of being selected.

Systematic Sample

A sample chosen from an ordered list by selecting every $k^{\text{th}}$ individual ($k = N/n$) after a randomly selected starting point between $1$ and $k$.

Stratified Sampling

A method where the population is divided into homogeneous strata based on common characteristics, and an SRS is selected from each group.

Cluster Sampling

A method where the population is divided into heterogeneous clusters and an SRS of clusters is selected, after which all items in the chosen clusters are sampled.