Level 4 Introduction to Quantitative Methods - Vocabulary Study Flashcards

Comprehensive vocabulary flashcards covering basic numeracy, algebraic methods, business statistics, and analytical tools for business decision-making.

Natural Numbers

All positive numbers starting from 1. Zero is not a natural number and the letter "n" denotes it in arithmetic expressions.

Whole Numbers

Includes all natural numbers and zero, with no decimal or fractional parts, and they never take negative values.

Integers

Numbers that include whole numbers and also negative numbers, representing only whole units without decimal or fractional parts.

Fractions

Parts of whole numbers indicating that one integer is being divided by another integer.

Decimals

Numbers based on the decimal (10s) system using a point to separate the ones place from the tenths place.

BEDMAS

An acronym representing the order of operations in complex numeric expressions: Brackets, Exponents, Division, Multiplication, Addition, and Subtraction.

Proper Fraction

A fraction in which the numerator is smaller than the denominator.

Improper Fraction

A fraction in which the numerator is larger than the denominator.

Mixed Fraction

A fraction consisting of a whole number alongside a fraction, where the whole number precedes the fraction.

Recurring Decimals

Fractions that do not divide easily and give the same number or series of numbers to infinity.

Standard Form

A way of expressing very small or very large numbers in a manageable form as $A \times 10^n$, where $n$ is an integer and $A$ is a number less than $10$.

Percentage

Derived from the Latin 'per centum', it means 'by the hundred' or 'per hundred', indicated by the symbol %.

Ratio

Expresses the relationship between two or more values with similar units of measurement, denoted by the colon (:) symbol.

Proportion

A mathematical statement consisting of two equal ratios, written with the symbol "::" and read as "as".

Principal

The original amount of a loan or investment.

Simple Interest

The interest calculated as a percentage of the principal amount only, typically for short duration loans or investments.

Compound Interest

Interest calculated on both the principal amount and the accumulated interest from previous periods.

Present Value (PV)

A financial concept used to calculate the worth of future sums of money in the present day based on a specific discount rate.

Depreciation

The reduction in the value of an asset over time due to wear and tear, obsolescence, or technological changes.

Straight-line Method

A method of depreciation that spreads the cost of an asset evenly throughout its useful life.

Reducing Balance Method

A method where depreciation for each year is calculated at a fixed rate on the diminishing value (Net Book Value) of the asset.

Variable

An unknown quantity in an algebraic expression represented by a letter whose value can change.

Constant

A value in a mathematical expression that is known and does not change.

Coefficient

The number that accompanies or precedes a variable in an algebraic expression.

Linear Equation

An equation where the maximum power of each variable is one and, when plotted on a graph, it forms a straight line.

Simultaneous Equations

A pair of equations used at the same time to determine the values of two unknown variables.

Quadratic Equation

An equation derived from a quadratic expression where the highest power of a variable is $2$, typically taking the form $ax^2 + bx + c = 0$.

Gradient

The slope of a line on a graph, represented by $m$ in the equation $y = mx + c$.

y-Intercept

The point where a straight line crosses the y-axis, represented by $c$ in the equation $y = mx + c$.

Statistics

A branch of mathematics focused on methods to systematically collect, organise, and analyse data to extract information for decision-making.

Descriptive Statistics

Statistical methods used for organising and summarising information.

Inferential Statistics

Statistical methods for drawing and measuring the reliability of conclusions about a population based on a sample.

Primary Data

Original data collected for the first time directly from fieldwork, such as surveys, interviews, or experiments.

Secondary Data

Data obtained from pre-existing published or unpublished sources such as journals, government reports, or news articles.

Discrete Data

Quantitative data generated by counting, which can only take finite values (usually integers).

Continuous Data

Quantitative data generated by measuring, which can take any value (including fractions and decimals) between two points.

Population

The complete set of people, objects, or institutions that is the subject of a statistical study.

Sample

An appropriately sized subset of a population selected for data collection to draw conclusions about the larger group.

Sampling Frame

A published source or list, such as a directory, from which a sample is selected.

Simple Random Sampling

A technique that gives all subjects in a frame an equal probability of being included in the sample.

Stratified Random Sampling

A technique involving dividing a population into subgroups (strata) and applying simple random sampling to each.

Cluster Sampling

Also called area sampling, it involves dividing the population into natural miniatures or 'clusters' and selecting whole clusters for the sample.

Nominal Level Measurement

A measurement scale used specifically for classification purposes where numerical values do not indicate importance or rank.

Ordinal Level Measurement

A measurement scale used for ranking elements based on preference or order.

Interval Level Measurement

A numeric scale with equal intervals used for ranking where zero is just one of many intervals (like temperature).

Ratio Level Measurement

A measurement scale where zero is a fixed point of significance, allowing values to be expressed as ratios of one another.

Frequency Distribution

A tabular classification showing the number of times (frequency) a variable takes each of its data values.

Bar Chart

A graph that visually presents categorical data and quantitative values using rectangular bars separated by spaces.

Pie Chart

A circular diagram used for presenting categorical data where segments represent proportions of 360 degrees.

Histogram

A display of numeric, continuous, and grouped data where vertical bars are contiguous (touching) and their area represents frequency.

Frequency Polygon

A line graph joining the mid-top points of a histogram to show the pattern of frequency distribution.

Ogive

A cumulative frequency curve that plots cumulative frequencies against the upper class boundaries of a distribution.

Stem and Leaf Plot

A diagrammatic summary of raw quantitative data that splits each value into a leading digit (stem) and trailing digit (leaf).

Arithmetic Mean

The average of all values in a data set, calculated as the sum of all values divided by the number of observations.

Median

The middle value in a distribution that splits the data into two equal halves when arranged by magnitude.

Mode

The value that occurs most frequently in a distribution.

Range

The simplest measure of dispersion, calculated as the difference between the largest and smallest values in a set.

Standard Deviation

The most popular measure of dispersion, denoted by the symbol $\sigma$, representing the distance between a value and the arithmetic mean.

Skewness

A measure of the asymmetry in a data distribution, indicating whether values cluster on one side of the mean.

Correlation

A statistical measure examining the linear relationship between paired data to see if variables move together in the same or opposite directions.

Scatter Diagram

A plot of independent and dependent variable observations on a graph to indicate the correlation and pattern between them.

Linear Regression

A statistical method used for modelling the relationship between two quantitative variables to make business forecasts.