Mathematics Glossary

Absolute error – The difference between the actual value and the measured value indicated by an instrument.

Accessibility sampling – Selecting a sample from onlythose items that we most readily available.

Acount servicing fee – Ongoing account keeping fees.

Actual interest rate – Represents the actual oercentage return per year on an investment (the simple interest rate per annum).

Addition rule of probability – For mutually exclusive events. P(either A or B) = P(A) + P(B). The general rule takes into account overlaps in activities; P(either A or B) = P(A) + P(B) – P(both A and B).

Adjacent side – The side next to the right-angle used for reference in a right-angled triangle. Adjacent sides usually found in triangles and other polygons.

Algebraic modelling – When a practical siteation is described mathematically using an algebraic function.

Angle of elevation – The angle through which you must look up from the horizontal to sight an object.

Allowable deduction – A deduction from taxable income permitted by the Government. Allowable deductions include expenditure substracted from gross income. Allowable deduction is to lower the amount of income subject to income tax

Allowance – An extra payment made to workers for working in outside of favourable conditions, such as travel allowances, overtime allowances, etc.

Analysing data – A process that interprets data and transformation it into information.

Angle of depression – The angle through which you must look down from the horizontal to sight an object, which is the angle between the horizontal and your line of sight when you are looking down.

Angle of elevation – The angle through which the observer must look up from the horizontal to the line of sight an object.

Angular distance – Angle made at the centre of the earth between two places.

Annual leave – A period of time that each permanent employee is allowed each year for holidays, and is paid time off work granted by employers.

Annual leave loading – An extra payment of a certain percentage, such as 17.5%, of the gross pay made to employees when they take their annual leave.

Annuity – A form of investment that involves the regular contribution of money.

Annulus – The area, a ring-shaped object, bounded by two concentric circles that have the same centre.

Appreciation – An increase in value of an item over time. It is often expressed as the rate of appreciation.

Arc length – Length of part of the circumference of a circle.

Area – The quantity of the two-dimensional space within the boundary of a closed figure.

Area chart – A graph consisting of different ‘areas’ each representing a data set over a period of time. The thickness of the area indicates the size of the data.

Asset – Item that is of value to the owner.

Bar graph – A graph where categorical data are displayed in horizontal bars, with the categories on a vertical axis and quantity on the horizontal axis.

Back bearing – Also called Reserve bearing .

Bearing – The direction one object is from another object. See Compass bearing abd True bearing.

Benchmark – Fixed point of reference for use in leveling.

Bias – When events are not equally likely.

Bimodal – A set of scores for which two scores occur most often.

Binomial distribution – Distribution resulting from repeated rials of an experiment that has only two outcomes (one called a success, the other called a failure).

Bivariate data – Sets of data containing two variables.

Bonus – An extra payment or gift earned as reward for achieving a goal.

Bottom plate – Timber of metal strip at the bottom of a frame.

Bow – Front of a boat.

Box-and-whisker-plot – A method of graphically displaying a five-number summary. The plot is drawn to scale with the box representing the interquartile range and the whiskers representing the range. Within the box, the median is also shown.

Brace – Sheets of timber, or strips of timber or metal used to provide strength to a frame and help the frame to retain its shape.

Brokerage – Charges made by a stockbroker for acting as an agent in the buying and selling of shares.

Breakeven point – The point of intersection when income equals costs in some practical problems.

Budget – A list of a person’s budget is made to try to avoid spending more than is earned. A balanced budget is where income equal expenditure.

Building square – A device whether corners of buildings are square.

Cadastral map – A map showingboundaries of land in a survey plan.

Capacity – The quantity of solid, liquid or gas that a 3-dimensional object could hold.

Capture-recapture sampling – A sample of the population is captured, ragged then released. Later another sample is obtained and the proportion of tagged items noted.

Casual rate – A higher rate of pay to compensate casual workers for the lack of holiday and sick pay.

Categorical data – Data which are not numerical and are put into categories such as types of car.

Causality – When the occurrence of one variable causes another. For example, there is a strong positive relationship between a person’s shirt size and shoe size but one does not cause the other. On the other hand, there is a strong positive relationship between the amount of a Lottery jackpot and the number of tickets sold. In this case, it would seem that one does cause the other.

Cell – The intersection of a row and a column in a table.

Census – Data gathered from the entire population.

Chance – The likelihood of an event occurring.

Circuit – Path which starts and finishes at the same node and in which no arc is traversed more than once.

Central tendency – A method for describing a typical score in a data set. There are three measures of central tendency – mean, median and mode.

Class centre – Median or middle score of a class in a grouped frequency distribution.

Closed cylinder – A cylinder with both circular bases.

Closed question – One that must be answered within given categories.

Cluster sampling – Selecting a sample from a cluster within a population.

Coastal lights – Short range lights used for indicating harbours and rivers.

Cocked hat – Intersection of position lines which form a small triangle which is circled and the time of fix noted because of small errors.

Coefficient – The number in front of a particular letter in an algebraic expression. For example, the term 2y has coefficient of 2.

Column graph – Similar to a bar graph, but the data are displayed in vertical columns.

Collecting data – A process that involves deciding what to collect, locating it and collecting it.

Commission – Payment made to a salesperson. A commission is usually paid as a percentage of sales.

Comparison rate – The interest rate on the loan that includes the interest and any fees or charges.

Compass bearing – A bearing that uses the four directions of the compass (north, south, east and west) such as N37E.

Compass error – Caused by damage to compass or exposure to magnetism and electricity. These deviations can be determined snd true bearing calculated.

Compass rose – Double circle on a chart indicating true and magnetic directions. The magnetic directions. The magnetic variation for that region is described in the inner circle. It is used to establish position lines on a chart.

Complementary events – Two events that cover all possible outcomes to a probability experiment. The sum of the probabilities to complementary events is 1.

Complementary shape – Two or more plane shapes.

Composite solid – Two or more common solids.

Compound events – When more than one activity is being considered at the same time.

Compound interest – Interest calculated from the initial amount borrowed or principal plus any interest that has been earned. It calculates interest on the interest.

Compound period – The length of time between interest in a compound interest investment.

Constant of variation – The rate at which two quantities vary.

Concentration – A measure of how much of a given substance is mixed with snother substance.

Cone – A solid figure, with a circular base, that tapers to a point.

Consumer Price Index (CPI) – Measure of variation in retail prices for goods and services which represent a high proportion of rxpenditure of households.

Contingency table – A 2-dimentional table that displays data in terms of two variables.

Correlation – Strength of the relationship between two vatiables.

Continuous data – Data which can take value within a given range.

Contour interval – Difference in altitude represented by each contour line on a map.

Contour lines – Imaginary lines that join points having the same heights above sea level.

Conversion graph – A graph used to change one quantity from one unit to another unit.

Cosine rule – Triginometric rule that relates the sides and angles in a triangle. It is used to solve triangle problems involving three sides and one angle.

Cosine ratio – The ratio of the adjacent side and hypotenuse in a right-angled triangle.

Course – A ‘course of bricks’ is an alternative expression for a ‘row of bricks’.

Credit card statement – Information sent to the credit card user each month. It includes an account number, opening balance, new charges, payments, refunds, reward points, payment due data, minimum payment and closing balance.

Credit card – A small plastic card used to buy goods and services and pay for them later.

Credit card statement – Information sent to the credit card user each month. It includes an account number, opening balance, new charges, payments, refunds, reward points, payment due data, minimum payment and closing balance.

Critical path – Pathe through the network along activities that cannot be delayed without delaying the entire project.

Cross bearing fix – Method of determining position by using the intersection of at least two position lines.

Cross section – The intersection of a solid with a plane.

Cubic function – A function in the from y = ax3. The graph of a cubic function is curve.

Cumulative frequency – A progressive total of the frwquencies.

Cumulative frequency histogram – A histogram with equal intervals of the scores on the horizontal axis and the cumulative frequencies associated with these intervals shown by vertical rectangles.

Cumulative frequency polygon – A line graph constructed by joining the top right hand corner of the rectangles in a cumulative frequency histogram.

Curing – Allowing concrete to dry slowly to increase its strength.

Cyclic trends – Trends that fluctuate up and down but not according to season.

Cylinder – A prism with a circular base.

Data – Information before it is processed.

Daily balance – The balance of an account considered each day.

Data set- Collection or group of scores.

Database – A processed and arranged set of data on a population.

Datum line – A level line to which other heights or levels are referenced.

Datum surface – A level surface to which other heights or levels are referenced.

Dead reckoning – Also deduced reckoning, or DR, is a method of estimating the position of a boat that does not involve a fix by sighting. This method uses previously collected information concerning speed and course direction.

Deventure – A legal document detailing an investment agreement.

Decile – A band of 10% of scores ina data set.

Declining balance depreciation – A method of depreciation ehrn the value of an item decreases by a fixed percentage each time period.

Deduction – A sum of money that a deducted from a worker’s gross payment before receiving net pay.

Degree – A unit for measuring angles.

Dependent variable – A variable whose value responds to changes in the independent variable.

Depreciation – The decrease in the value of an item over time.

Directed network – A network that consists of arcs that have a direction indicated on them.

Directed measurement – Measurement obtained from data collected by surveys, experiments or observations.

Direct vcariation – Relationship between two variable when one variable depends directly on another variable.

Discrete data – Dataobtained when a quantity is counted. It can only take exact numerical values.

Displaying data – A process that involves the presentation of the data and information.

Distributive law – A rule for expanding grouping symbols by multiplying each term inside the grouping symbol by the number or term outside the grouping symbol.

Devided bar graph – A graph that shows the relationship or proportions of parts to a whole. The bars or rectangles are drawn to scale.

Dividend – A payment given as an amount per share or as a percentage of the issued price.

Dividend yield – The annual dividend devided by the share’s market price and expresses as a percentage.

Dot plot – A graph that consists of a number line with each data point marked by a dot. When several data points have the same value, the points are stacked on top of each other.

Double time – A penalty rate which pays the employee twice the normal hourly rate.

Double stem-and-leaf plot – A stem-and-leaf plot that used two sets of similar data together.

Double stem-and-whisker plot – A box-and-whisker plot that uses two sets of similar data together.

Doubling-the-angle-on-the-bow method- Method which estimates position: say, of a boat at sea, using isosceles triangle properties.

Drop – A vertical length. The term is commomly used in wallpapering and curtaining.

Dumpy level – Levelling device used on construction sites.

Earliest completion time – Earliest time in which all activities can be completed.

Earliest start time – Earliest time that an activity can start after all prior activities have been completed.

Effective interest rate – The equivalent interest rate if compounding happened annually.

Effective width – The width of a sheet, taking into account overlap between adjacent sheets.

Elevation – A scale drawing of what a building will look like from one side.

Ellipse – Oval shaped plane figure.

Enlargement – A figure is drawn similar to, but larger than the original. The corresponding sides will be in equal ratio and all corresponding angles will be equal.

Errors of deviation – The sum total of errors of a magnetic compass due to surrounding influences excluding magnetic variation.

Equally likely outcomes – These occur when each element of the sample space for a probability experiment is equally likely to occur.

Equation – A mathematical statement that says that two things are equal.

Equator – Imaginary horizontal line that divides the earth into hernisphere. Latitude of the equator is 0 degree.

Event – An occurrence that is being examined in a probability experiment.

Excess flow capacity – The flow capacity through an arc minus the flow into an arc.

Exchange rate – The rate at which currencies can be interchanged. The buying rate refers to the rate at which banks will buy the currency from you. Selling rate to the rate banks will sell you a currency.

Expand – Remove the grouping symbols.

Expected outcome – The number of times the outcome should occur. It is calculated by multiplying the probability of the event and the number of trials.

Expected value (mathematical expectation) – The expected gain or loss in a game of chance.

Experimental function – A function in the form \( y = b(a)^x\). If \(a \gt 1 \) then the function represents exponential growth. If \( 0 \gt a \gt 1 \) then the function represents exponential decay.

Expression – A mathematical statement written in numbers and symbols.

Exponential graph – A graph whose shape is a smooth curve which gets progressively steeper.

Extrapolate – Extend a graph to make predictions about future or past trends beyond the end points of the graph.

Extrapolating – Extending a graph to make predictions.

Evaluate – Work out the exact value of an expression.

Extrapolate – To extend a graph so as to make predictions about future trends.

Face value – The initial price when a company firs lists on the stock exchange (ASX).

Failure (in a binomial experiment) – Not obtaining a successful outcome in a binomial experiment.

Factorise – To break up an expression into a product of its factors.

Favourable – Elements from the sample space that meet the requirement for an event to occur.

Fibonacci sequence – A sequence of numbers where each new number is the result of adding the two previous numbers – 1, 1, 2, 3, 5, 8, 13, 21, …

Field diagram – A diagram used to calculate the area of irregularly shaped blocks of land.

Financial expectation – The expected amount of money to be achieved in a game.

Five-number summary – A summary of a data set consisting of the lower extreme, lower quartile, median, upper quatile and upper extreme.

Fix-by-four-point bearing – Adaptation of doubling the angle on the bow method. If the initial bearing used is 45, the final bearing is 90.

Fixing position – Process of determining location of a vessel at any time.

Flat rate loan – Loan that uses simple interest.

Flashing – Pattern of a light emitted by a light-house. It has a number of short flashes of light followed by a long period of darkness.

Floats – Processes involving the initial raising of shareholder’s funds and listing of a company on the share market.

Floats time – The maximum time an activity can be deffered without delaying the entire project.

Floor plan – A plan showing the floor dimensions of a structure and detailed dimensions of features such as a door, windows, wall thicknesses and stairs.

Flow capacity – The total possible flow through a network.

Formular – A mathematical relationship between two or more variables.

Fortnight – Two weeks or 14 days.

Footings – Trenches (in the shape of rectangular prims) dug around the perimeter of a slab, and sometimes within the slab as a support for internal walls.

Four points bearing – An adaptation of the doubling the angle on the bow method used by navigators when the angle on the bow is 45 degree.

Frequency – The number of time an event occures.

Frequency histogram – A graph suitable for statistical (quantitative) data. It is a column graph drawn with score or class centres on the horizontal axis and frequency on the vertical axis. A half unit (half column width) space is drawn before the first column with no other gaps between columns.

Frequency polygon – A line graph often drawn on the same axes as a frequency histogram. The line is drawn from the corner of the axes to the centre of each column.

Frequency table – A table displaying statistical data. For ungrouped data, the table will have columns for a score, tally, frequency and possibly the cumulative frequency. For grouped data, the score column will be replaced with a class column and a clas centre column.

Fundamental counting principle – The number of elements of the sample space for a multi-stage probability experiment is found by multiplying the number of ways each stage can occur. This is the fundamental counting principle.

Future value – The amount to which an investment will grow under compound interest.

Future value of an annuity – The sum of money contributed plus the compound interest earned.

Gable roof – In the shape of an inverted “V” with two rectangular surfaces.

General form – A linear equation written in the form \( ax + bx + c = 0 \).

Goods and Services Tax (GST) – A tax that is levied on the price of all items other than fresh food. The GST is levied at a rate of 10%.

GPS (Global Positioning System) – A satellite navigation system accessed by users on land, sea or in the air, operated by the US Department of Defense.

Gradient – The rate of increase (or decrease) in the dependent variable per one unit increase in the independent variable.

Gradient intercept formular – A linear equation written in the form \( y = mx + b\).

Great circle – A circle of the greatest possile diameter that can be drawn on the surface of a sphere.

Greenwich Mean Time (GMT) – The standard time in Greenwich which is used as the basis for calculating the time in all other parts of the world.

Greenwich Meridian – The meridian of longitude from which angular distances in the east-west direction are measured. Using the longitude calculated from the Greenwich Meridian, time in different places on the Earth’s surface is calculated.

Grid reference – The code used to describe position on a topographic map.

Gross income – The total amount of money earned from all sources. It includes interest, profits from shares or any payment received throughout the year.

Gross pay – A person’s earnings before any deductions are taken out.

Group certificate – see PAYG Payment Summary Statement.

Group data – A data set tabulated in small groups rather than as individual scores.

Grouping symbol – Symbols used to indicate the order of operations such as parentheses ( ) and bracket [ ].

Grout – A mixture rubbed between tiles to provide separation and to bind them together.

Gyro compass – A compass with a spinning gyroscope which aligns with the true north-south axis of the Earth (as opposed to the magnetic compass which aligns itself with the magnetic north pole).

Hand bearing compass – A hand-held compass.

Harbour lights – Lights including buoys and beacons which indicate entrances to ports and harbours at night.

Hip roof – Generally consists of two trapezium shaped surfaces and two triangular surfaces.

Histogram – A column graph which displays the frequency for a set of scores.

Horizontal – Level, flat and parallel to the horizon or the ground.

Hyoerbolic function – A function in the form \(y = \dfrac{a}{x}\). The graph of a hyperbolic function is curve.

Hyportenuse – The longest side of a right-angled triangle. The hypotenuse is opposite the right angle.

Income – Money received by a person that is taxable and is usually in exchange for labour of the result of an investment.

Independent – Two events are independent if the occurrence of one has no effect on the occurrence of the other.

Income tax – Tax thant is paid on all income received.

Independent variable – A variable whose value does not depend on the value of another variable.

Index notation – A method to write expressions in a shorter way such as \(a \times a = {a^2}\).

Indirect tax – Any tax that is not paid directly to the government by the taxpayer. For example, the GST is an indirect tax because it is paid to the retailer who then passes it on to the government.

Inflation – A rise in the price of goods and services or Consumer Price Index (CPI). It is often expressed as annual percentage.

Inflow – The inflow of a node is the total of all arcs flowing into the node.

International Date Line – The meridian of longitude opposite to the Greenwich Meridian. The International Date Line is, however, bent for convenience. When crossing the International Date Line, the date changes.

Intercept – The position where the line cuts the axes.

Interest – The amount paid for borrowing money or the amount earned for lending money.

Interest rate – The rate at which interest is charged or paid. It is usually expressed as a percentage.

International date line – An imaginary line through the Pacific Ocean that corresponds to 180 degree longitude.

Interpolate – Drawing a graph using data found at the end points.

Interquarile range – A number that represents the spread of a data set. The interquartile range is calculated by subtracting the lower quartile from the upper quartile.

Inverse variation – Relationship between two variable when one variable increases while the other variable decreases.

Inestment bonds – A form of investment offered by a bank or the government where the interest is paid on the investment at regular agreed intervals of time.

Judgmental sampling – A sample selection based on the judgment of those making the selection.

King post – Vertical post from the horizontal tie beam of a truss to the apex of the truss

Knot – A unit for measuring speed at sea. It is defined as one nautical mile per hour.

Laser level – Device which emits horizontal rays of laser light.

Laser start time – The latest time an activity may be started without delaying the entire project.

Latitude – The angular distance of a point on the Earth’s surface either north or south of the equator.

Leveling – Surveying process of determining the relative heights of points on the Earth.

Lighthouse – A prominent elevated construction located on the coastline which emits a long-range flashing light (also known as lights).

Like term – Term with exactly the same pronumeralss such as 3a and 6a.

Limit of reading – The samllest unit on measuring instrument.

Linear metre – Length expressed in metres.

Line of the best fit – A line drawn on a scatterplot that passes through or is close to as many points as possible.

Line of latitude – A small circle on the surface of the Earth whose plane is parallel to the equator.

Line of longitude – A semi-circle passing over the Earth’s surface from the true north to the true south pole (also knows as a meridian).

Linear equation – An equation whose variables are raised to the poser of 1.

Linear function – A function when graphed on a number plane is a straight line.

Linear modelling – A mathematical description of a practical situation using a linear function.

Linear regression – The process of fitting a straight line to the data.

Lintel – A timber or metal strip above a door or window.

Loan – Amount borrowed.

Loan application fee – Costs in setting up a loan.

Loan establishment fee – Initial costs in processing the loan application.

Loan repayment – The amount of money to be paid at regular intervals over the time period.

Longitude – The angle or angular distance on the earth’s surface east or west of the Greenwich meridian.

Lower extreme – The lowest score in the data set.

Lower quartile – The lowest 25% of scores in a data set.

Magnetic compass – A device which aligns itself with the Earth’s magnetic north-south line.

Magnetic north – The position on the Earth’s surface of the north pole of the Earth’s internal magnet.

Magnetic variation – The angle between true north and direction of north as determined by a compass in that region.

Major axis of an ellipse – Longest axis. It passes through the centre of the ellipse.

Market value – Current price of a share.

Mean – The average of a data set, found by totaling all the scores then dividing by the number of scores.

Measurement – Determining the size of a quantity.

Median – The middle score or average of the two middle scores in a data set.

Median regression line- A linear regression that involves dividing the data into three groups, finding the median of each group and drawing a line between the medians.

Medicare levy – A payment made as part of our tax system that covers the cost of basic health care services, The basic levy is 1.5% of gross income; however, low-income earners pay the levy at a reduced rate.

Mercator’s projection – A cylindrical projection where points from a sphere are projected onto the walls of the cylinder in mapping.

Meridian of longitude – A line on the Earth’s surface that runs from the North Pole to the South Pole. Each meridian of longitude is measured by the number of degree east or west it is of the Greenwich Meridian.

Minimal spanning algorithm – A systematic method used to find the minimal spanning tree or the smallest tree.

Minimum monthly balance – The lowest balance in an account during the month.

Minor axis of an ellipse – Shortest axis. It passes through the centre of the ellipse.

Minute – A measure of time or an angle. There are sixty minutes in one hour and one degree.

Mode – The score in a data set with the highest frequency.

Morgage – A loan given to buy a house or unit.

Mortar – A mixture of cement and sand used to bind bricks together (and keep them a fixed distance apart).

Multimodal – Data with many modes or peaks.

Multi-stage event – This occurs when there is more than one part to a probability experiment. For example, tossing two coins can be considered as tossing one coin then tossing another, therefore there are two parts to this experiment.

Mutually exclusive events – Two events are mutually exclusive if they cannot happen at the same time.

Nautical mile – A unit of length used to measure distances along great circles. It is used by sea and air navigators.

Negatively skewed – Data more on the right side. The long tail is on the left side (negative side).

Net of a solid – A drawing consisting of plane shapes that can be folded to form a solid.

Net pay – The amount of money actually received by the employee after all deductions have been subtracted from the gross pay.

Network – An arrangement of arcs and nodes.

Node – Part of na network represented by a circle that indicates the end or start of an arc: sometimes called a vertex.

Nogging – Horizontal separators between studs in a fram.

Normal distribution – Data with the same mean, mode and median.

Nominal data – Categorical data which have no order associated with them.

Nominal interest rate – The interest rate that is nominated in compound interest format. It may be expressed as compounding over any period of time (daily, monthly7, quarterly…)

Non-compliant response – A response that does not fit within the expected responses or categories provided in a questionaire.

Non-linear graph – A graph which is not a straight line.

Normal distribution – Such a distribution occurs when a data set is symmetrically distributed about the mean.

Number pattern – A sequence of numbers formed using a rule. Each number in the pattern is called a term.

Numerical data – Data which involve numbers or measurments.

Occulting – A flashing light pattern where periods of light exceed periods of darkness.

Odds – The ratio of the number of ways of losing to the number of ways of winning.

Offset survey – A survey involving the measurement of distances along a suitable diagonal or traverse. The perpendicular distances from the traverse to the vertices of the shape are called the offsets.

On – Odds for events with a probability greater than a half, expressed as a ratio of winning ways to losing ways.

Offset method – Method of surveying using lines perpendicular to survey line.

Open cylinder – A cylinder without a circular base. It is the cured part of the cylinder.

Open qustions – One that has no guidelines within which to answer.

Opposite – The side opposite to the angle used for reference in a right-angled triangle.

Ordered selection – A selection made from a group of items and the order is important. Also called a permutation.

Ordinal data – Categorical data that are associated with some qualitative scale.

Ordnance level – An official datum level.

Ordinary rate – The normal hourly rate for a wage earner.

Organising data – A process that arranges, represents and formats data. It is carried out after the data is collected.

Outflow – The outflow of a node is the minimum of the inflow and the sum of the capacities of arcs leading from the node.

Outcome – A possible result to a probability experiment.

Outlier – Data values that appear to stand out from the main body of a data set.

Overtime – This is when a person earns more than the regular hours each week.

Pascal’s triabgle – A pattern of numbers used in probability theory.

Path – A series of nodes connected by arcs.

Parallel of latitude – A line on the Earth’s surface parallel to the equator. Each parallel of latitude is measured in terms of the angular distance either north or south equator.

PAYG – Pay As You Go. The method usually applied to the collection of tax.

PAYG Payment Summary Statement – A statement of gross income and the PAYG tax deducted from that income throughout the financial year. It is given to the employee by the employer at the end of each financial year.

Payment by piece (Piecework) – Payment for the amount of work completed.

Penalty rate – A higher of pay made to a person who is working overtime.

Per annum – per year.

Periodical investment – An amount of money invested on a regular basis at fixed time intervals.

Permanent survey marks – Bronze plaques or other marks placed by surveyors as permanent reference point.

Persentage chance – The probability of an event expressed as a percentage.

Persentage error – The maximum error in a measurement as a percentage of the measurement given.

Persentile – A band of 1% of score in a data set.

Perimeter – The distance around the boundary of a figure.

Pitch – The angle the roof makes with the horizontal.

Pitch ratio – The pitch of a roof expressed as a tangent ratio in the form 1 : x.

Plane table survey – A map is drawn on a level table which is on the field being surveyed. Methods include relation, intersection or triangulation and traversing.

Polygon – A many sides figure.

Population standard deviation – A calculation for the standard deviation that uses all the data or the entire population
\( \sigma _n\) .

Positively skewed – Data more on the left side. The long tail is on the right side (positive side)

Plumb bob – A device consisting of a length of string with a weight attached at one end. It is used to test whether a surface is vertical.

Polygon – A line graph displaying the frequency for a set of scores.

Population – An entire group of people or objects to which a statistical inquiry is applied.

Port – Left hand side of the vessel.

Prefix – The first part of a word. In measurement it is used to indicate the size of a quantity.

Prsent value of an annuity – The amount of money if invested now would equal the future value of the annuity.

Principal – The initial amount of money borrowed.

Price earnings ratio (PE Ratio) – Calculated as a ratio of the market price of the share to the yearly earning of the share (dividend)

Prime meridian – The line of longitude (0 degree) passing through Greenwich. The locations of all other meridians are measured by the number of degrees east or west of the line.

Prism – A solid shape with a constant cross section.

Probability – A number between 0 and 1 that describes the chance of an event occurring.

Probability histogram – A column graph displaying the probability of the outcomes.

Probability tree diagram – Tree diagram in which the probabilities are listed on each branch of the tree.

Profile – Cross section showing the surface of the ground.

Profile level – The survey taken by a surveyor when heights of various positions are taken and recorded.

Pronumeral – A letter or symbol used to represent a number.

Pyramid – A solid shape with a plane shape as its base and triangular sides meeting at an apex.

Pythagoras’ theorem – In a right-angle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

Pythagorean triad or Pythagorean triple – Sets of three numbers which satisfy Pythagoras’ theorem.

Quadrant – Quarter of a circle. The arc of a quadrant measures 90 degree.

Quadrant function – A function in the form \(y = a{x^2} + bx + c \). The graph of a quadratic function is curve in the shape of a parabola.

Qualitative data – Data which do not involve numbers or measurment.

Quantitative data – Data which can be measured. A numerical value can be assigned to them.

Quartile – 25% of the data set. The upper quartile is the 25% of the data set and the lower quartile is the bottom 25% of the data set.

Questionnaire – A set of questions completed for a statistical investigation.

Quota sampling – The selected sample conforms to a set quota (specified number)

Radar chart – A graph to compare the perfomance of one or more entities. It has the appearance of a spider web.

Radial suevey – A survey that involves measuring the angles and sides from a central point.

Randon sample – A sample that occures when members of the population have an equal chance of being selected.

Rafter – Beam at the top of a truss to which the roof cladding is attached.

Random trends – Those trends which occur randomly caused by external events such as wars, floods.

Range – A number which represents the spread of a data set. The range is calculated by subtracting the smallest score from the largest score.

Rate – A comparison of different quantities in definite order.

Rate of interest – Percentage of interest per annum.

Ratio – A comparison of different quantities in definite order.

Recording error – Where data have been incorectly recorded.

Rectangular distribution – When graphed, this type of distribution produces a rectangular shape.

Reduction – A similar figure, drawn smaller in size than the original.

Reducing balance loan – Loan calculated on the balance owing on the initial amount of money borrowed.

Regression line – A line of best fit that is extrapolated to make predictions about data.

Reinforcing mesh – Steel mesh laid in the concrete in the footings and slab to provide structural strength.

Relative error – A measurment calculated by dividing the limit of reading (absolute error) by the actual measurement.

Relative frequency – A number between 0 and 1, usually a decimal, which describes how often an event has occurred. The relative frequency is found by dividing the number of times an event has occurred by the total number of trials.

Rest – Length of a compounding period.

Retainer – A fixed payment usually paid to someone receiving commission. They receive the retainer regardless of the number of sales made.

Reverse bearing – The bearing of B from A is the reverse bearing of A from B.

Roulette – A game of chance where a ball is placed into a spinning wheel with numbered slots.

Roof truss – Frame providing shape and strenth for a roof.

Running fix – A method of navigation used to estimate position when only one shore object is available. Two-position lines at the shore object, taken at different times, and the vessel’s speed are required for this method.

Royalty – A royalty is a payment made to the owner of copyright such as a musician or author. The royalty is usually a percentage of sales.

Salary – A form of payment where a person is paid a fixed amount to do their job. A salary is usually based on an annual amount divided into weekly or fortnightly installments.

Salvage value – The depreciated value of an item.

Sample – When data are gathered from a position of the population, that is taken to be representative of the whole population.

Sample space – A list of all possible outcomes to a probability experiment.

Sample standard deviation – A calculation for the standard deviation when the data set is a sample \( \sigma _{n – 1} \).

Scale factor – A number by which the side lengths on the first of two similar figures is multiplied by to obtain the measurements on the second of the figures.

Scatterplot – A graph that shows two variables, one on each axis, and their relationship by plotting the points generated by each data pair.

Score – Each piece of quantitative data is a score.

Seasonal trend – A trend that fluctuates with the changing seasons.

Segmented – A bar graph showing the bar broken up into categories (segments).

Scientific notation – A number between 1 and 10 multiplied by a power of ten. It is used to write very large small numbers more conveniently.

Sector – The area between any teo radii of a circle.

Sector graph – A graph where a circle is cut into sectors. Each sector then represents a section of the data set. Each sector is the same proportion of the circle as the part of the data set it represents.

Secular trend – A trend that appears to either increase or decrease stadily over time, with no major changes of direction.

Semi-major axis – A line from the centre of the ellipse to the boundary along the major axis.

Semi-minor axis – A line from the centre of the ellipse to the boundary along the minor axis.

Semicircle – Half a circle. The arc of a semicircle measures 180 degree.

Share market – The market dealing with share trading.

Shares – Where a share in a company can be purchased through the Stock Exchange. The share entitles the owner to vote at company meetings and to receive a share in the company’s profits in the form of a dividend.

Shortest path algorithm – A systematic procedure to find the shortest path between two nodes in a network.

Significant figures – A statement to specify the accuracy of a number. It is often used to round a number.

Similar (figures) – Two or more figures with corresponding angles equal and corresponding sides in the same ratio.

Simple interest – A fixed percentage of the amount invested and is calculated on the original amount.

Simpson’s rule – A formula to estimate the area of a shape with an irregular boundary.

Simulation – A mathematical model that represents a real experiment or situation.

Simultaneous equations – Two or more equations whose values are common to all the equations. It is the point of intersection of the equations.

Sine rario – The ratio of the opposite side and the hyponding in a right-anfled triangle.

Sine rule – Trigonometric rule that relates the sides and angles in a triangle. It is used to solve triangle problems involving two sides and two angles.

Site plan – A plan showing the boundaries of a block of land and the position of the structure on the plot.

Skewed data – Data not symmetrical.

Slab – Foundation for a structure.

Small circle – A circle that is drawn on the surface of a sphere that is of a smaller diameter than a great circle.

Smoothness – Data whose graph has no breaks or jugged sections.

Smoothness – Data whose graph has no breaks or jugged sections.

Spanning tree – Connects all nodes in the network and does not contain any loops.

Sphere – A closed surface consisting of point in space that are a fixed distance, the radius, from a given point, the centre.

Spirit level – A device, usually constructed of aluminum, containing a vial of liquid with an air bubble. It can be used to determine whether a surface is horizontal and whether a surface is vertical.

Spread – A measure of how the scores are spread out from the mean.

Square numbers – Those numbers that can be represented as a pattern of dots in the shape of a square; e.g. – 1, 4, 9, 16, …

Stamp duty – A tax payable to the government on the transfer of property from one name to another.

Standard deviation – A measure of the spread of a data set. The standard deviation is found on a calculator using either the population standard deviation or the sample standard deviation .

Standard normal tables – A set of tables giving the area under a normal curve between two particular z-scores.

Standard score – (also called z-score) A figure that represents the distance of a score from the mean in terms of the standard deviation. The standardized score is the number of standard deviations that a member of the data set is from the mean.

Statistics – Numerical facts compiled to describe a data set.

Statistics inquiry – A process of gathering statistics that involves six steps: posing questions, collecting data, organising data, displaying data, analysing data and writing a report

Starboard – The right-hand side of the vessel.

Stem-and-leaf-plot – A method of displaying a data set where the first part of a number is written in the stem and the second part of the number is written in the leaves.

Stern – The rear of the boat.

Strata – A group within a population that reflects the characteristics of the entire population.

Stratified sampling – Selecting a sample with the same proportion of characteristics as is present in the population, for example, the same percentage of men and women.

Straight line depreciation – A method of depreciation when the value of an item decreases by the same amount each time period.

Straight line method – The depreciation of an item is calculated by subtracting a constant amount from the value each year.

Still – Timber of metal strip below a window.

Stratified sample – A sample using categories or strata of a population. Members from each category are randomly selected. For example, one student is selected from each year 7, 8, 9, 10, 11 and 12.

Staffs – Piles used on a survey line.

Studs – Vertical strips of timber or metal in a frame.

Subject of the formula – When a formula or equation has a pronumeral with no numbers on the left hand side of the equal sign, such as \(C = 40n + 75\), then C is the subject of the formula.

Substitution – It involves replacing the pronumeral in an algebraic expression with one or more numbers.

Success (in a binomial experiment) – Obtaining a successful outcome in a binomial experiment.

Superannuation fund – Type of annuity where money is invested for a person’s retirement.

Surface area – The sum of the area of each surface of the solid.

Summary statistic – A number such as the mean, median or mode which describes a data set.

Survey -A questionnaire conducted on a sample (a proportion of the population).

Survey line – The initial line set out in the field. All positions in the field are measured with reference to this line.

Survey plan – A plan showing all boundaries of blocks of land and the position of roadways.

Symmetrical – Data that formes a mirror image of itself when folded in the ‘middle’ along a vertical axis.

Symmetry – Data evenly balanced about the centre.

Systematic list – An oderly method of determining all the possible outcomes.

Systematic sample – A sample that divides the population into a structured sample size. For example, sorting the names of people in alphabetical order and selecting every 5th person.

Tangent ratio – The ratio of the opposite side and the adjacent in a right-angled triangle.

Taxable income – The amount of income upon which the amount of tax due is calculated. Taxable income is calculated by subtracting any allowable tax deductions from the total gross income.

Temporary benchmark – A reference point on the Earth’s surface selected by a surveyor for a particular task.

Term – The period of time for the investment or loan.

Term deposit – An amount of money that is deposited for a fixed period of time (term).

Term of the loan – The length of time over which the loan is agreed to be repaid.

Theodolite – Surveying instrument that allows measurement of angles in horizontal and vertical of the surface of the Earth.

Three-dementional – Can be described using three measurements (for example a length, a width and a height).

Tie beam – Beam at the base of a truss.

Time and a half – A penalty rate where the employee is paid 1.5 times the normal hourly rate.

Time series – Bivariate data where one of the variables is time.

Time zone – The gross income minus any allowable deductions.

Top plate – Timber or metal strip at the top of a frame.

Topographic map – Detailed sketch of a portion of the Earth.

Transit fix – A method of determining position using a transit line.

Transit line – The line of sight connecting an observer and two prominent shore objects.

Tree – A network which has two loop.

Tree diagram – A method of listing the sample space to a multi-stage probability experiment. The diagram branches once for each stage of the experiment at each level showing all possible outcomes to each stage.

Trend line – A straight line used to represent a time series.

Trial – The number of times a probability experiment has been conducted.

Triangular numbers – Those numbers that can be represented as a pattern of dots in the shape of an equilareral triangle.

Triangulation – Surveying method that allows a survey around obstacles.

Trigonometry – A branch of mathematics in which sides and angles of triangles are calculated.

True bearing – A bearing using the angle measued clockwise from the north, around to the required direction, such as 120 degree.

True north – The northern location of the Earth’s axis of spin.

Two-dimentional – Can be described using two measurements (for example a length and a width).

Two up – A game of chance which involves tossing two coins and betting on the outcome.

Two transit fix – A method of position determination using the intersection of two transit lines.

Two-way tables – A table that presents data using rows and columns.

Unimodal – Data with only one mode or peak.

Unitary method – A method used in ratio and percentages involving the calculation of a unit.

Unordered selection – A selection made from a group of items and the order is not important. Also called a combination.

Upper extreme – Highest score in the data set.

Upper quartile – The highest 25% of the scores in the data set.

Valuation fee – SCosts in the assessment of the market value of a property.

Value Added Tax – Similar to the GST, a VAT is levied in many countries on the cost of goods and services. The rate of VAT varies from country to country.

Variable – A symbol used to represent a number or group of numbers.

Volume – The amount of space contained in, or occupied by, a 3-D object.

Venn diagram – A Venn diagram is made up of a rectangle that represents all possible outcomes, with the other activities represented by circles drawn within the rectangle.

Wage – Aform of payment that is based on an hourly rate.

Water level – A device consisting of a length of clear hose filled with water. It can be used to establish levels between two points which are separated levels by some distance.

x-intercept – The point at which the group cuts the x-axis.

y-intercept – The value of y when a function crosses the vertical axis.

z-score – A standardised score used to compare scores in a normal distribution.

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