sac 1 statistics & data analysis terms T1-4

This flashcard set includes key vocabulary and concepts in statistics and data analysis with their definitions for exam preparation.

68-95-99.7% Rule

A rule for determining the percentage of values that lie within one, two, and three standard deviations of the mean in a normal distribution.

Allocation

The process of assigning tasks to different members of a group to complete tasks efficiently.

Bar Chart

A statistical chart used to display the frequency distribution of categorical data.

Bivariate Data

Data where each observation records information about two variables for the same subject.

Boxplot

A graphical display of the five-number summary showing outliers if present.

Categorical Variable

A variable that represents characteristics of individuals, such as eye color or place of birth.

Centre of Distribution

A measure of location in a distribution, including mean and median.

Centring

The process of adjusting smoothed values to align with original data values.

Coefficient of Determination (r²)

A coefficient measuring the predictive power of a regression line.

Continuous Variable

A numerical variable representing a quantity that is measured rather than counted.

Correlation Coefficient (r)

A statistical measure of the strength of the linear association between two numerical values.

Cycle (Time Series)

Periodic movement in a time series over a period greater than a year.

Data Transformations

Using a mathematical rule to change the scale on an axis to linearize a scatterplot.

Deseasonalise

The process of removing seasonality from a time series.

Discrete Variable

A numerical variable determined by counting, such as the number of people in a queue.

Dot Plot

A statistical graph using dots to display individual data values on a number line.

Explanatory Variable (EV)

In bivariate data, the variable used to explain or predict the response variable's value.

Extrapolation

Using a model to make predictions outside the range of the original data.

Five-number Summary

A list including the minimum, first quartile, median, third quartile, and maximum.

Frequency Table

A list showing the values a variable takes along with their occurrences.

Histogram

A statistical graph for displaying the frequency distribution of a numerical variable.

Interpolation

Using a regression line to make predictions within the range of explanatory variable values.

Interquartile Range (IQR)

Defined as IQR=Q3 - Q1, it measures the spread of the middle 50% of data.

Irregular Fluctuations

Unpredictable fluctuations present in any real-world time series.

Least Squares Method

A technique for finding regression line equations that minimizes the sum of squares of residuals.

Linear Regression

The process of fitting a straight line to bivariate data.

Log Scale

A scale used to transform skewed histograms to symmetry or linearize scatterplots.

Logarithmic Transformations

Transformations that linearize scatterplots by compressing the upper end of scale.

Lower Fence

A threshold for identifying outliers in a dataset.

Mean (x̄)

The balance point of a data distribution, calculated as x̄=∑x / n.

Median (M)

The middle value in a data distribution that divides an ordered dataset into two equal parts.

Modal Category

The category or interval that occurs most frequently in a dataset.

Mode

The value that occurs most frequently in a dataset.

Modelling

The use of a mathematical rule to represent real-life situations.

Moving Mean Smoothing

A technique where original data values are replaced by the means of values around them.

Moving Median Smoothing

Smoothing a time series plot using moving medians instead of means.

Negatively Skewed Distribution

A data distribution with a long tail to the left.

Nominal Variable

A categorical variable used for naming only, such as eye color.

Normal Distribution

A bell-shaped data distribution where the 68-95-99.7% rule applies.

Numerical Variable

A variable representing quantities that are counted or measured.

Ordinal Variable

A categorical variable that allows for both naming and ordering.

Outliers

Data values that stand out from the main body of a dataset.

Parallel Box Plots

Box plots drawn side-by-side for comparing distributions.

Percentage Frequency

Frequency expressed as a percentage of the total.

Positively Skewed Distribution

A data distribution with a long tail to the right.

Quartiles

Statistics that divide an ordered set into four equal groups.

Range (R)

The difference between the smallest and largest observations in a dataset.

Reciprocal Transformations

Transformations that compress the upper end of the scale more than log transformations.

Reseasonalise

Converting seasonal data back to its original form.

Residual

The vertical distance from a data point to the fitted regression line.

Residual Plot

A plot of the residuals against an explanatory variable.

Response Variable (RV)

The primary variable of interest in a statistical investigation.

Scatterplot

A graph used to display bivariate data where data pairs are represented by points.

Seasonal Indices

Indices that quantify seasonal variations in data.

Seasonality

The tendency for values in a time series to vary predictably based on time periods.

Segmented Bar Chart

A graph that displays information contained in a two-way frequency table.

Shape of Distribution

The general form of a data distribution, described as symmetric, positively or negatively skewed.

Slope (of a straight line)

Defined as slope = Δy / Δx, it is also known as the gradient.

Smoothing

A technique used to reduce random variation in a time series to make underlying patterns (such as trends or seasonality) easier to see.

Spread of a Distribution

A measure of data values' clustering around a central point in the distribution.

Squared Transformations

Transformations that stretch out the upper end of the scale on either axis.

Standard Deviation (s)

A summary statistic measuring the data's spread around the mean.

Standardised (z) Scores

Scores indicating the distance and direction of a data value from the mean.

Statistical Question

A question that depends on data for its answer.

Stem Plot

A method for displaying data by splitting each observation into a stem and leaf.

Strength of Linear Relationship

Classified as weak, moderate, or strong, determined by scatter in a scatterplot.

Structural Change (time series)

A sudden change in the established pattern of a time series plot.

Summary Statistics

Numerical values representing features such as centre and spread of a data distribution.

Symmetric Distribution

A data distribution where values are evenly spread around the mean.

Time Series Data

A collection of data values recorded at specific times.

Time Series Plot

A line graph plotting values of a response variable in time order.

Trend

The tendency for values in a time series to increase or decrease over time.

Trend Line Forecasting

Using a line fitted to a time series to predict future values.

Two-Way Frequency Table

A table classifying subjects according to two categorical variables.

Univariate Data

Data associated with a single variable.