Business Analytics Chapter 2 - Descriptive Statistics Flashcards

Vocabulary flashcards covering key terms, data types, visual analytics methods, measures of central location and variability, and association metrics from Chapter 2 of Business Analytics.

Data

Facts and figures collected, analyzed, and summarized for presentation and interpretation.

Variable

A characteristic or a quantity of interest that can take on different values.

Observation

A set of values corresponding to a set of variables.

Variation

The difference in a variable measured over observations.

Random Variable

A quantity whose values are not known with certainty; also referred to as an uncertain variable.

Population

Consists of all the elements of interest in a statistical study.

Sample

A subset of the population, consisting of elements selected from it.

Random Sampling

A sampling method that allows gathering a representative sample from the population data.

Quantitative Data

Data for which numeric and arithmetic operations, such as addition, subtraction, multiplication, and division, can be performed.

Categorical Data

Data for which arithmetic operations cannot be performed.

Cross-Sectional Data

Data collected from several entities at the same, or approximately the same, point in time.

Time Series Data

Data collected over several time periods.

Experimental Study

A study in which a variable of interest is identified, and one or more other variables are controlled or manipulated to obtain data about how they influence the variable of interest.

Observational Study

A nonexperimental study that does not attempt to control the variables of interest, such as a survey.

Conditional Formatting

An Excel tool that makes it easy to identify data satisfying specific conditions within a data set.

Frequency Distribution

A summary of data showing the number (frequency) of observations in several nonoverlapping classes, typically referred to as bins.

Relative Frequency Distribution

A tabular summary of data showing the relative frequency for each bin, calculated as the bin frequency divided by total observations $n$.

Percent Frequency Distribution

A tabular summary that summarizes the percent frequency of data for each bin, providing estimates of relative likelihoods of different values.

Histogram

A graphical presentation of quantitative data constructed as a column chart with no spaces between columns, where horizontal base represents class limits and vertical height represents frequency measure.

Frequency Polygon

A graphical display useful for comparing quantitative distributions that uses lines to connect the frequency counts of observations from different bins.

Cumulative Frequency Distribution

A variation of the frequency distribution showing the number of data items with values less than or equal to the upper class limit of each class.

Mean

The most common measure of central location, computed as the average of all data values: $\bar{x} = \frac{\sum x_i}{n}$.

Median

The value in the middle of a data set when data are arranged in ascending order, serving as the preferred measure of central location for highly skewed data.

Mode

The value in a data set that occurs with the greatest frequency.

Bimodal Data

A data set that possesses exactly two modes.

Multimodal Data

A data set that possesses more than two modes.

Geometric Mean

A measure of central location calculated by finding the $n\text{th}$ root of the product of $n$ values: $x_g = \sqrt[n]{(x_1)(x_2)\dots(x_n)}$.

Range

The simplest measure of variability, defined as: $\text{Range} = \text{Largest Value} - \text{Smallest Value}$.

Sample Variance

A measure of variability based on squared deviations about the mean, calculated as $s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}$.

Standard Deviation

The positive square root of the variance ($s = \sqrt{s^2}$), which measures variability in the same units as the original data.

Coefficient of Variation

A relative measure of variability expressing the standard deviation as a percentage of the mean: $\left(\frac{\text{Standard Deviation}}{\text{Mean}} \times 100\right)\%$.

Percentile

The $p\text{th}$ percentile is a value such that at least $p\%$ of items take on this value or less, and at least $(100 - p)\%$ take on this value or more.

Quartiles

Specific percentiles dividing data into four equal parts: $Q_1$ (25th percentile), $Q_2$ (50th percentile/median), and $Q_3$ (75th percentile).

Interquartile Range (IQR)

The difference between the third quartile and first quartile: $\text{IQR} = Q_3 - Q_1$.

z-Score

A standardized value denoting the number of standard deviations a data value $x_i$ is from the mean $\bar{x}$, computed as $z_i = \frac{x_i - \bar{x}}{s}$.

Empirical Rule

A rule for bell-shaped distributions stating that $\sim 68\%$ of values fall within $1\,s$ of the mean, $\sim 95\%$ within $2\,s$, and almost all within $3\,s$.

Outlier

An unusually small or unusually large value in a data set, typically evaluated as a candidate when its $z\text{-score}$ is less than $-3$ or greater than $+3$.

Boxplot Structure

A graphical summary of a data distribution constructed using five key elements: $Q_1$, median, $Q_3$, interquartile range (IQR), whiskers, and identified outliers.

Scatter Chart

A graph for analyzing the relationship between two quantitative variables.

Sample Covariance

A descriptive measure of linear association between two variables, calculated as $s_{xy} = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{n - 1}$.

Covariance Linear Relationships

Visual scatter plots displaying positive linear relationship ($s_{xy} > 0$), no linear relationship ($s_{xy} \approx 0$), and negative linear relationship ($s_{xy} < 0$).

Sample Correlation Coefficient

A measure of the strength and direction of linear association between two variables, defined as $r_{xy} = \frac{s_{xy}}{s_x s_y}$, ranging between $-1$ and $+1$.