NOTES ON ALL PRELIM TOPICS.doc

Preliminary Exam Preparation, Study Notes

Table of ContentsChapter One: Linear Equations and Functions.......................................................................................................2

Algebraic Terms..................................................................................................................................................2

Formulas.............................................................................................................................................................2

Expanding Expressions.......................................................................................................................................2

Solving Equations...............................................................................................................................................2

Equations Involving Algebraic Fractions.............................................................................................................2

Equations and Formulas.....................................................................................................................................2

Linear Functions.................................................................................................................................................2

The Gradient as a Rate of Change......................................................................................................................3

Linear Modelling.................................................................................................................................................3

Chapter Four: Statistical Samples and Displays......................................................................................................4

Statistical Investigations.....................................................................................................................................4

Interpreting Graphs............................................................................................................................................4

Types of Data......................................................................................................................................................4

Sample Types......................................................................................................................................................4

Sampling techniques..........................................................................................................................................4

Constructing graphs............................................................................................................................................5

Misleading graphs..............................................................................................................................................5

Frequency histograms and polygons..................................................................................................................5

Dot plots.............................................................................................................................................................5

Stem and Leaf plots............................................................................................................................................5

Radar Charts.......................................................................................................................................................5

Chapter Five: Ratios and Similar Figures.................................................................................................................6

Simplifying Ratios...............................................................................................................................................6

The Unitary Method...........................................................................................................................................6

Dividing a Quantity into a Given Ratio................................................................................................................6

Scale Factors and Centre of Enlargement...........................................................................................................6

Properties of Similar Figures...............................................................................................................................6

Using Shadows and Similar Triangles..................................................................................................................6

Maths Preliminary Study Notes 29.08.08

Scale Drawings....................................................................................................................................................6

Floor Plans and Elevations..................................................................................................................................7

Symbols and Calculations from Plans and Elevations.........................................................................................7

Chapter Six: Earning and Taxation..........................................................................................................................8

Wages, salaries and overtime.............................................................................................................................8

Commission, Piecework and Royalties...............................................................................................................8

Bonuses and Allowances....................................................................................................................................8

Gross and Net Pay..............................................................................................................................................8

Household Bills...................................................................................................................................................9

Budgeting...........................................................................................................................................................9

Income tax..........................................................................................................................................................9

Goods and Services Tax......................................................................................................................................9

Chapter Seven: Trigonometry..............................................................................................................................10

Pythagoras’ theorem........................................................................................................................................10

Investigating the Tangent Ratio........................................................................................................................10

Investigating the Sine Ratio..............................................................................................................................10

Investigating the Cosine Ratio..........................................................................................................................10

Mixed Problems................................................................................................................................................10

Bearings............................................................................................................................................................10

HELP PAGES 246 to 287................................................................................................................................11

Chapter Eight: Rates and Linear Modelling..........................................................................................................12

Rates.................................................................................................................................................................12

Rate Problems..................................................................................................................................................12

Speed and Fuel Consumption...........................................................................................................................12

Converting Rates..............................................................................................................................................13

Graphing Linear Functions................................................................................................................................13

Direct Linear Variation......................................................................................................................................13

Conversion Graphs...........................................................................................................................................13

Linear Modelling...............................................................................................................................................14

Chapter Nine: Probability.....................................................................................................................................15

The Language of Probability.............................................................................................................................15

Outcomes and Sample Spaces..........................................................................................................................15

Multistage Events.............................................................................................................................................15


Performing Simple Experiments.......................................................................................................................15

Experimental Probability..................................................................................................................................15

Theoretical Probability.....................................................................................................................................15

Complementary Events....................................................................................................................................15

Chapter Ten: Savings and Investment..................................................................................................................16

Simple Interest.................................................................................................................................................16

Compound Interest..........................................................................................................................................16

Account Fees and Charges................................................................................................................................16

Investing in Shares............................................................................................................................................16

Inflation and Appreciation................................................................................................................................16

Chapter Eleven: Statistical Measurement............................................................................................................17

Measure of Central Tendency: Mean, Median and Mode................................................................................17

Finding Averages from Statistical Displays........................................................................................................17

Using a statistical calculator given separate scores..........................................................................................17

Comparing Averages.........................................................................................................................................17

Quartiles, Deciles and Percentiles....................................................................................................................17

Dispersion: Range and Interquartile Range, Standard Deviation......................................................................18

Boxplots............................................................................................................................................................18

Cumulative Frequency Graphs..........................................................................................................................18


Chapter One: Linear Equations and Functions

Algebraic TermsAn algebraic expression is a general statement involving pronumerals. Pronumerals are letters of the alphabet that stand for numbers. An algebraic expression is made up of terms.

When adding or subtracting it is important to remember to only add or subtract ‘like terms’.

When multiplying terms with powers of the same base, add the powers. When dividing terms with powers of the same base, subtract the powers.

FormulasA formula is an algebraic rule describing a relationship between pronumerals. For example, the volume of a cylinder has the formula

where r represents the radius of the cylinder’s base and h is its height. This means that the volume of the cylinder is the product of ‘

, the radius squared and the height.

Expanding ExpressionsAlgebraic expressions involving grouping symbols (brackets) can be expanded and simplified. Expanding means rewriting the expression ‘the long way’ and removing the grouping symbols.

Solving EquationsAn equation contains an algebraic expression and an equals sign. To solve an equation, we find the value of the pronumeral that makes the equation true. The process of solving an equation requires the use of inverse (opposite) operations. To solve an equation you must:

1. Perform inverse operations on both sides of the equation2. Aim to have the pronumeral on one side and a number on the other. E.g. x=12

Equations Involving Algebraic FractionsFor equations involving algebraic fractions, both sides can be multiplied by a common multiple of the denominators, found by multiplying the denominators together. This way, we convert all fractions into whole numbers and then solve the equation the usual way.

Equations and FormulasSometimes when solving a problem involving a formula, the answer is not immediately found after substituting into a value. Instead an equation results, which must then be solved.

Linear FunctionsTo calculate the gradient of a line you use the formula m=


. A linear function forms a graph that creates a straight line. A linear function has the form y=mx+b, where m and b are constant numbers. A linear function has 2 terms: mx is called the linear term as it contains the variable x

(but not raised to a power), while b is called the constant term because it is just a number (no variable).

Any function containing higher powers of x such as are called non-linear functions. When a linear function is written in the form of y=mx+b, its gradient and y-intercept are

easily identified. The gradient is m and the y-intercept is b. A positive gradient means that the graph is sloping upwards (left to right) A negative gradient means the graph is sloping downwards (right to left) A gradient of -2 means that as the x-values increase by 1, the y values decrease by 2. To

draw a gradient of -2 on the number plane, move across 1 unit (as usual), but then go down 2 units.

The Gradient as a Rate of ChangeThe gradient of a function is the rate of change of y. The gradient is not only a measure of steepness of a line, but also a measurement of how quickly y values change. The higher the gradient, the steeper the line and the faster y changes relative to x. When a line is horizontal it is evident that there is a ‘run’, but no ‘rise’. With vertical lines this is opposite with no ‘run’ and a ‘run’.

Linear ModellingThe graph of a linear function (y=mx+b) is a straight line, demonstrating that the variable y is changing at a steady rate. In fact, as x increases by 1 unit, y increases by m units. Because the value of units. Because the value of y depends on the value of x, y is called the dependant variable and x is called the independent variable. For y=mx+b, the gradient (m) is the rate of change of y, and the vertical intercept (b) is the value of y when x=0. If a observed number pattern suggests a linear relationship, then we use the linear function y=mx+b to model the situation, this is called a linear model.



Chapter Four: Statistical Samples and Displays

Statistical Investigations In statistical investigations there are three main stages including:1. Collect and organize information or data2. Summarise and display this data3. Analyse and interpret this data

Interpreting Graphs See page 116 for graph and explanation. No notes!!!

Types of Data Categorical Data –obtained form a categorical variable is information that can be put into categories that are distinct or arranged in some order (for example, ‘do you own a pet?’, the answer is a ‘yes’ or ‘no’)Numerical data is obtained from a numeric variable and is information represented by numbers. The data can be discrete or continuous.

Discrete: obtained through a counting process. The possible values are clearly separated from each other.Continuous: obtained through a measuring process. The possible values are on a continuous scale.

Sample Types Samples are often conducted when a population s too large or difficult to survey. A population refers to the total amount of items under consideration. There are three types of random samples including:1. Simple random sample: each member of the population is equally likely to be

chosen, so the sample has the attributes of the whole population. For example, names drawn out of a hat or winning balls in lotto are picked by a tumbler.

2. Systematic sample: the first member of the survey is chosen at random, then the others chosen at regular intervals. For example, every 20th light bulb is taken from a conveyer belt for testing.

3. Stratified sample: the population divided into equal strata or layers, and then a random sample is taken from each strata or layer.

Sampling techniques Sampling techniques include random numbers which can be used to simulate a variety of situations. To use a table of random numbers, chose any starting point, them move systematically up, down or diagonally.


Another example of a sampling technique is Bias and non-random sampling. Bias usually occurs in a non-random sample favoring one section of the population.

Constructing graphs Data represented graphically is visually appealing, and we are more likely to notice paterns if data is represented in a statistical graph. A statistical display should be simple and interesting and make an impact, but should not mislead the reader.

Misleading graphs Statistical graphs are often used to display information in a way that may mislead the reader. Advertisers use graphs to entice us to buy products, and company directors often use graphs to display statistical information to their advantage when dealing with shareholders or prospective clients.

Frequency histograms and polygons A histogram is used to represent quantitative data and is a column graph with no spaces between the columns. The height of each column is represents the frequency of the scores. See page 143.

Dot plots A dot plot is a simplified type of histogram. It is easy to see where clusters of scores occur and each score is represented by a symbol, usually a dot. See page 147.

Stem and Leaf plots See page 149. A stem and leaf plot is represented by a column showing tens (stem) and ones (leaf) for example 4(stem) and 3(leaf) equates to a score of 43.

Radar Charts Divide all outcomes by 360 degrees. If more then more, use separate color and indicate this. Label the graph


Chapter Five: Ratios and Similar Figures

Simplifying RatiosThe parts of a ratio are called terms. A simplified ratio is one where the terms are whole numbers with not common factor. To simplify a ratio, we divide or multiply each of its term by the same number.

The Unitary MethodThe unitary method can be used to solve problems involving ratios. The unitary method considers the value of one part and uses this to calculate other parts.

Dividing a Quantity into a Given RatioWhen dividing the value of the parts of a quantity divided into a given ratio, we can use the unitary method or consider each part as a fraction of the whole quantity.

Scale Factors and Centre of EnlargementSimilar figures are the same shape but not necessarily the same size.

All figures similar to a given figure will be an enlargement or reduction of that figure.

The scale factor shows by how much a figure is enlarged or reduced. The original figure is called the object and the enlarged figure is called the image. The matching angles in each figure are equal to preserve the same shape. Two similar figures that have a scale factor of 1 are said to be congruent. A centre of enlargement (page 172 for example) will help one to draw similar

figure.

Properties of Similar Figures Similar figures have all matching angles equal. Similar figures have matching sides in the same ratio.

Using Shadows and Similar TrianglesOn a sunny day, a sick of known length, such as a metre rule, and a long tape can be used to determine the height of trees, flagpoles or buildings in your neighbourhood with the aid of similar triangles. The stick is often referred to as a shadow stick. One way of finding the height of an object is by using the formula:

=

Scale DrawingsA scale drawing is usually a reduction of a real object, such as a building, but can be an enlargement of a very small object, such as a computer chip. The scale factor used in a scale


drawing is called the scale. Some common scale drawings are house plans and maps. Examples of ways used to represent scales include; 10mm to 1m, 25:1, 1:100, 1cm = 2m and so on.

Floor Plans and Elevations When an architect is drawing up two-dimensional plans for a new home, the view from the top looking down is called the floor plan or plan, and the views from the front, back and sides are called elevations. The plan is a scale drawing of the floor of the house. Yeah, (HELP?).

Symbols and Calculations from Plans and ElevationsNo notes on this section, simply interpretations of graphs starting on page 188. Due to this and the fact that I’m special, I need HELP.


Chapter Six: Earning and Taxation

Wages, salaries and overtime A wage is a payment calculated on the number of hours worked in a given period of time, usually weekly. People who engage in manual or mechanical work earn a wage. The more hours they work the more pay they receive. A salary is a fixed payment quoted as a yearly amount but paid weekly, fortnightly or monthly. People who engage in clerical and professional work earn a salary. Overtime pay is paid to a wage earner who works beyond normal hours. Salary earners are not paid extra for overtime but may receive fringe benefits.

Commission, Piecework and Royalties Not all workers are paid according to the amount of time they work. Commission (earned by salespeople and agents) is calculated on the value of items sold. Piecework (earned by dressmakers, fruit pickers and craftspeople) is calculated on the number of items made or processed. Royalties (earned by writes, composers and inventors) are calculated on the number of copies sold or made of their creative piece of work.

Bonuses and Allowances A bonus is paid to employees who produce work of a high quality or volume. An allowance is paid to employees who either incur expenses in their line of work or work under dangerous conditions. Annual leave loading is extra pay given during annual leave (usually 4 weeks at Christmas time). It is paid at a rate of 17.5% of 4 weeks normal pay. A government allowance is paid by the Federal government to people who aren’t financially secure, such as the old, young, sick and unemployed.

Gross and Net Pay Everyone who earns an income pays a percentage of it to the government as income tax. The government collects these taxes to fund public programs and services such as schools. Income tax is


usually deducted from a persons everyday pay know as PAYE tax. NET PAY=GROSS PAY – TAX – OTHER DEDUCTIONS

Household Bills Features of a household bill include: 1. Account number: Your customer ID2. Account period: The period of service covered by your bill3. Amount due, Dater Due: The amount to be paid and the due date4. Last bill: The amount charged on the last bill.5. Your payment: The amount paid on the last bill6. Fixed charges: Constant fees or charges for using the service7. Variable charges: charges based on the amount of the service used

Budgeting A budget is a plan for managing your income wisely. A budget is divided into two sections: income and expenses. A balanced budget has its total expenses equal to its total income.

Income tax The tax rate operates on a sliding scale. Not all income is taxed. For example, deductions can be made from work related expenses. Once this is subtracted one can work out their total taxable income. TAXABLE INCOME = INCOME – ALLOWABLE (TAX) DEDUCTIONS

Goods and Services Tax Since the year 2000 there has been GST added to most items. GST tax is on spending unlike income tax which is on earning.


Chapter Seven: Trigonometry

Pythagoras’ theorem Pythagoras noted that the hypotenuse is the longest side of a right-angled triangle and is always opposite the right angle. He also noted that the square of the hypotenuse is equal to the sum of the squares of the other 2 sides. This is simplified through the formula

. When using the formulas you should:1. Draw a rough diagram if one is not provided.2. Decide whether the hypotenuse or shorter side needs to be found.3. Check whether the answer looks reasonable: compare it to the diagram.4. Make sure that the hypotenuse is the longest side, or a shorter side is not longer then

the hypotenuse.

Investigating the Tangent Ratio To find an angle inside the triangle when we have the opposite side and the adjacent side we can use the formula

Investigating the Sine RatioTo find an angle inside the triangle when we have the opposite side and the hypotenuse we can use the formula

Investigating the Cosine RatioTo find an angle inside the triangle when we have the adjacent side and the hypotenuse we use the formula

Mixed ProblemsWhen solving trigonometric problems involving right-angled triangles, it is important to indentify which trigonometric ratio is appropriate. In order to aid this process, students often remember the phrase “SOH-CAH-TOA”.

BearingsBearings use angles to show the direction of one location form a given point. For example, the bearing of Sydney to Narrabri is 166 degrees. This means that, from Narrabri, the direction of Sydney


is 166 degrees measured clockwise form north. True bearing, are written as 3-digit angles ranging from 000 degrees to 360 degrees.

HELP PAGES 246 to 287 Pasted from <file:///C:\Documents%20and%20Settings\c.baird\My%20Documents\School\2008\Term%20Three\Maths\Preliminary%20Exam\Preliminary%20Exam%20Summaries.docx>


Chapter Eight: Rates and Linear Modelling

RatesA rate is a measurement that compares two different quantities. The table shows examples of some rates and their units.

Rate Units

Heartbeat beats/minutes

Population growth persons/year

Speed kilometres/hour

Cost of meat/fruit dollars/kilogram

Fuel consumption of motor vehicle

litres/100km

Concentration of pesticide grams/kilogram

Rate ProblemsRate problems can sometimes be solved using the unitary method. When using the unitary method we find one part first and multiply it be the necessary number to find the answer. When mixing a solution of medicine, nurses and pharmacists need to make sure it contains the right amount of the drug. When mixing a batch of pesticide, a farmer needs to make sure it is of the correct strength. The concentration of a substance is the amount of the substance compared to the whole mixture or solution. Concentration can be expressed as a rate or a percentage. If expressed as a rate, it takes one of the following forms:

weight pert weight (w/w): for solids mixed with solids (e.g. grams/kilogram for fertilizer)

weight per volume (w/v): for solids dissolved in liquids (e.g. milligrams/millilitre for drugs)

volume per volume (v/v): for liquids mixed with liquids (e.g. millilitres/litre for fuel)

Speed and Fuel Consumption Speed is the rate at which something is moving or changing. The following formula can be manipulated to find either speed, distance or time by using the normal step to solve an equation.Speed

Fuel consumption is the rate at which a vehicle uses petrol, measured in litres per 100 km. A car with fuel consumption of 8.6L/100 km uses 8.6L of fuel to travel 100 km. The lower the rate, the better the fuel consumption.


Converting RatesAs km/h to m/s is a common conversion, the following graph may be handy to remember.

÷3.6

Graphing Linear FunctionsIn Chapter One, we examined the linear function y=mx+b.

Because the value of y depends on the value of x, y is called the dependant variable and x the independent variable.

The graph of y=mx+b is a straight line, demonstrating that y changes at a steady rate. In fact, m, the gradient of the line, is the rate of change of y. As x increases by 1 unit, y

increases by m units. The value of b is the y-intercept or vertical intercept of the line, and represents the

value of y when x is zero.

Direct Linear Variation To solve a direct variation problem:

Identify the two variables (say x and y) and form a variation equation, y=kx. Substitute values for x and y to find k, the constant of variation. Rewrite y=kx using the value of k. Use y=kx to solve the problem. See Page 208 for examples. HELP

Conversion GraphsConversions graphs involve interpreting graphs. A conversion graph is used to convert between different units, such as between metric and Imperial, and in foreign currency exchange. Most conversion graphs are line graphs that go through (0,0), so their equations are of the y=kx and hence


are examples of direct variation.

Linear ModellingModelling is the use of mathematics to describe a pattern or relationship that occurs in real life. Sometimes, the model may only be an approximation of a situation that is more complex. A model may take the form of an algebraic formula, a table of values or a graph. If it follows a linear relationship of the form y=mx+b, then it is called a linear model. HELP p.313. A line of best fit represents most or all of the points as closely as possible, goes through as many points as possible, has roughly half of the outlying points about it and roughly half of the outlying points below it and is drawn so that the distance between each outlying point and the line is kept at a minimum. Pasted from <file:///C:\Documents%20and%20Settings\c.baird\My%20Documents\School\2008\Term%20Three\Maths\Preliminary%20Exam\Preliminary%20Exam%20Summaries.docx>


Chapter Nine: Probability

The Language of ProbabilityWhen we consider how likely something is to happen we look at past experience or history, or gamily genetics, and sometimes we even use our gut feelings. Some events are certain to occur and some will never occur, but most are somewhere in between.

Outcomes and Sample SpacesAn outcome is the result of an experiment or game. A sample space is the set of all possible outcomes. An event is a group of one or more outcomes. We assume that all outcomes of an experiment or game are equally likely unless we know otherwise. There are many reasons for outcomes not being equally likely.

Multistage EventsIn an experiment consisting of more than one stage, multiply the number of outcomes possible at each stage to get the total number of outcomes in the sample space. For example, in a three-stage event, if there are m outcomes at the first stage, n outcomes at the second stage and p outcomes at the third stage, there are m x n x p outcomes in the sample space.

Performing Simple Experiments Performing simple experiments or playing games involving change will help you understand the probability of an event happening (or not happening) and whether or not outcomes are equally likely.

Experimental Probability The experimental probability of an event is the relative frequency of the event obtained through a game or an experiment.

Theoretical Probability The theoretical or calculated probability of an event is a mathematical measure of the likelihood of the even occurring.

. (E = event, S = sample space).

Complementary EventsWe have looked at the probability of an event occurring and will now look at the probability of an event not occurring. This is called the complementary event. An event and its compliment ‘go together’ to form a whole. The sum of the probabilities of two complementary events is 1.

P(event occurring) + P(event not occurring) = 1 P(event not occurring) = 1 – P(event occurring) P(E) = 1 – P(E1) where E and E1 are complementary events


Chapter Ten: Savings and Investment

Simple Interest Interest is money earned from an investment. The original amount invested is called the principle, and simple interest occurs when the interest is calculated as a percentage of this principle. SIMPLE INTEREST = PRINCIPAL × INTEREST RATE × TERM

Compound Interest Simple interest is only used when the investor collects the interest earned, such as a term deposit. Compound means “combine” and compound interest is when interest is calculated on your interest. The compound interest formulas are:A = P(1+r)n and I = A – P

Account Fees and Charges Banks and credit unions impose fees and charges on their savings accounts, for situations such as: 1. Excessive withdrawals made in a month2. Accounts with low balances3. ATM withdrawals made at other ATM machines4. Dishonored cheques5. Overdrawn accounts

There is also Government Debts Tax (GDT) on cheque withdrawals.

Investing in Shares When someone invests in a company they own part of that company. The companies annual profit is divided amongst all shareholders and each share of profit is called a dividend. The original price of a share is called its face value while the current price is called its market value or market value. DIVIDEND YIELD = DIVIDEND PER SHARE × 100%MARKET PRICE OF SHARE

Inflation and Appreciation Calculating price rises after inflation is an application of increasing an amount by percentage: but if the inflation rate remains constant, the we can use the compound interest ‘final amount’ formula [A = P(1+r)n].



Chapter Eleven: Statistical Measurement

Measure of Central Tendency: Mean, Median and ModeThe mean, median and mode are three summary statistics used to indicate the middle or centre of a set of data. They are known as averages or measures of central tendency. For a quantitative (or numerical) data set, the centre is usually described by the mean or median.

Mean is the arithmetic average. Insert formula from page 400. Median is the middle score when the scores are arranged in order.

For qualitative (or categorical) data set, the centre is usually described by the mode:

Mode is the score (or category) occurring the most times.

Finding Averages from Statistical DisplaysWhere data is displayed in a table, chart or graph, it is important to determine how many scores are represented before attempting to find the mean, median or mode.

Using a statistical calculator given separate scores1. set your calculator to statistics mode2. clear any previous data (memory)3. enter each score and press the M+ key after entering the score4. check you have entered the scores by pressing the n key, this number should equal the total

amount of scores in the data set, if not restart and clear memory5. press the average key (line above the x)

Comparing AveragesThe three distributions show the relative position of each measure of central tendency in a symmetrical or skewed frequency distribution. The ‘tail’ in a skewed distribution tell you the direction of the skew. Suppose, for example, that the diagrams represent the results in three different Maths tests. Then:

(a) represents a standard test where class results are evenly spread (b) represents a difficult test where most of the class results are low (c) represents an easy test where most of the class scores are high

Quartiles, Deciles and PercentilesDeciles, quartiles and percentiles refer to specific percentages of a distribution of scores. A distribution can be divided into 100 percentiles, 10 deciles or 4 quartiles.

Quartiles: Total distribution = 100% = 4 quartiles, 1 quartile = 25 percentiles = 25% of the


distribution. Deciles: Total distribution = 100% = 10 deciles, 1 decile = 10% of the distribution. Percentiles: Total distribution = 100% = 100 percentiles, 1 percentile = 1% of the distribution.

Dispersion: Range and Interquartile Range, Standard Deviation Range: Range = highest score – lowest score, the range represents the total spread of scores

but is not a good measure if there are outliers. Some data sets have the same range but are spread differently.

Interquartile Range: Interquartile Range = upper quartile – lower quartile, the lower quartile is the value below which 25% of the population lie. The upper quartile is the value above which 25% of the population lie. When a distribution has outliers, the interquartile range is a better measure of spread. It takes into account the middle 50% of scores and ignores and very high or very low scores.

Standard deviation: Standard deviation is the most common summary statistic used to measure spread. It’s found by taking the average of the squared deviations from the mean, and then finding the square root. The deviation of a score from the mean is the difference between the score and the mean.

BoxplotsA boxplot or box and whisker plot is a good visual representation of data, with the ‘box’ representing the middle 50% of scores and the ‘whiskers’ extending to the extremes. In boxplots, if an outlier exists, you may exclude this from the boxplot and represent it by a point. To draw a boxplot you need to make a five-number summary:

the lower extreme or smallest score the upper extreme or largest score the median the lower quartile or 25th percentile (Q1) the upper quartile or 75th percentile (Q3)

Cumulative Frequency GraphsThe cumulative frequency of a score is obtained by adding the frequencies up to and including that score. A cumulative frequency histogram or polygon plots scores against cumulative frequency. A cumulative frequency polygon is also called an ogive. Pasted from <file:///C:\Documents%20and%20Settings\c.baird\My%20Documents\School\2008\Term%20Two\Maths\In%20Class%20Tests\In%20Class%20Test,%20Monday%202.6.08.docx>
