Scientific Processes Summarized Notes #One

Learning objectives

At the end of this unit, you should be able to:
- perform simple arithmetical calculations: add, subtract, multiply and divide
- use averages, decimals, fractions, percentages, ratios and reciprocals
- use usual mathematical instruments (ruler, compasses, protractor, set square)
- recognise and use direct and inverse proportion
- use positive, whole number indices in algebraic expressions
- solve equations of the form x = y + z and x = yz for any one term when the other two are known
- make observations accurately, use appropriate techniques, handle apparatus/material competety and have due regard for safety
- distinguish between independent, dependent and constant variables
- state the hypothesis or aim of the investigation in relation to dependent and independent variables
- locate, select and organise information from a variety of sources
- record results ot experimental investigations in a logical manner (tables or graphs) and explain the importance of units and recording results of experimental investigations
- present each column of a table by heading it with the physical quantity and the appropriate unit, eg, times (units should be in the heading of the column and not in the measurements in the column)
- record entries in tables with constancy in terms of signiticant figures
- complete tables of data, and process data, using a calculator where necessary
- select suitable scales and axes for graphs
- draw charts and graphs from given data. It may have one or several curves plotted on it
- label each axis with the physical quantity and the appropriate unit, e.g. time/s
- plot the independent variable on the x-axis (horizontal axis) and plot the dependent vaniable on tie (vertical axis)
- present points on the curve clearly marked as crosses (x)or encircled dots (•). If a further curve is included , vertical crosses (+) may be used to mark the points
- label each graph with the appropriate heading (by convention always the dependent versus independent variable)
- interpret charts and graphs.

 The laboratory
A laboratory is a vworkroom that is used for scientific investigations. It can be a dangerous place with hazards from organisms, chemicals, equipment, apparatus, machines, gas and electricity. You need to know how to conduct yourself when you are in the laboratory and how to handle chemicals and equipment. Let us look at general laboratory techniques.

Laboratory protection and hygienee
- When in the laboratory, wear a cotton laboratory coat, correctly buttoned up, before you start your experiment, so as to protect yourself. You should have access to eye shields, gloves, dust face-masks and safety screens to use when needed. Wash your hands before and after the experiments. Do not eat, drink or smoke in the laboratory.
- Make arrangements to have a tutor or teacher in the laboratory when you are doing your experiments. Unsupervised work is forbidden. A tutor or teacher must be present at all times.
- You should know where the first-aid kit is and have an understanding of approved first-aid emergency treatments.
- If you happen to spill chemicals or break a beaker or test-tube, report it immediately and throw them in a special refuse disposal. Make sure you turn off water and gas taps, and electric switches after use.
- Wipe down bench tops after use with a disinfectant solution that can be obtained from your tutor.
- Clean and wash pieces of equipment after use and return them to their correct place.
- Do not intertere with experimental work that does not concern you. Leave the laboratory tidy.
- In a laboratory, there are two types of glassware:
• the soft glass, which is cheap, melts easily and may crack if heated suddenly
• the nard Pyrex glass, which is more expensive and does not melt easily or crack on heating.
- Glassware includes, glass rods, tubing, test-tubes, beakers, flasks, filter funnels, watch glasses, specimen bottles and Petri dishes. You need to wash these glasses in warm detergent solution (dilute hydrochloric acid), rinse and dry, or leave to air dry. Make sure to wear gloves when you pick up glass pieces.

Hardware
These are mainly iron or wood apparatus, namely iron tripod supports, retort stands, clamps and boss heads, and wire gauze. Wood used for filter funnel stands and test-tube racks.

 Heaters and heating techniques
- Heat is a form of energy needed for chemical and biological processes. There are four main kinds of gas burners: natural gas, Oil burners, botled liquid petroleum gas, and coal gas burners.
- Check what type of gas burner is in the laboratory.
- Connect the burner correctly to the gas tap, pressing the connecting gas tubing firmly over the burner inlet and gas-tap outlet to prevent leakage of gas.
- Light the gas correctly and quickly.
- Regulate the height of the gas flame, and regulate the air inlet to produce a quiet burning flame of medium heat.
- Small ethanol spirit burners consisting of a glass container and wick can be used where there is no gas supply.

Gas burner heating technique
Gas burners are sources of direct heat that can be applied directly to hard glass (Pyrex) test tubes, which must be supported by a test-tube holder. The test-tube should not be more than one-third full of water or solution, and its open mouth must be directed away from yourself or other people. The test-tube should be shaken throughout the heating process. There must be wire gauze between a glass beaker or flat-bottomed flask and the supporting tripod stand; beakers and flasks must not be heated with a direct gas burner flame. Contents of beakers - water and aqueous solution - should be stirred gently with a glass rod during heating. Wear protective eye shields to prevent hot liquid splashing outwards from the beaker while it is heating or boiling. Only water and aqueouS solutions of substances (that is, substances dissolved in water) can be heated by these methods. Ethanol, which is flammable, cannot be heated in this way.
Water bath heating technique
Small amounts of flammable liquid, such as ethanol, must always be heated indirectly in a water bath. Biological processes require heat energy, and function best at around 35-40°C. This is achieved by using a bath of warm water, the temperature of which is carefully noted with a 0-110 °C thermometer. The water bath can be a beaker, a metal pan or a small saucepan, heated by gas or electrically. If the water bath temperature rises too rapidly, it can be cooled down by adding small amounts of cold water. A learner should be able to maintain the water bath temperature within 2 °C of the working temperature, which i5 38 or 40 °C for a 40 °C working temperature. Special gas-regulating thermostats are inserted in the water bath to control the bath temperature automatically.

Handling plants and animals
Living organisms, whether large or small, must be handled with care, since many wild animals and microorganisms are sources of disease and infection. Strong gloves must be worn and any bites or scratches must be treated immediately by a doctor. Use plastic forceps with blunt points to pick up large objects, such as seeds, and forceps with fine points to pick up flower parts. Pooters are used to pick up small insects. Small objects in water can be picked up with a dropper pipette fitted with a teat. Dissection instruments must be washed in hot, soapy water and disinfected after use, and kept in a cloth instrument roll.
Cleaning the microscope
Microscopes are valuable and expensive biological instruments. Lenses should not be touched with the fingers and should be dusted with a microfibre cloth. Always keep the microscope under its cover when not in use. Soft paper tissues can be used to dry a wet lens.
 Cleaning glassware
Sterilisation of equipment is often necessary. This is done by heating equipment in a pressure cooker or autoclave with water for 20 minutes. Glassware and metalware can be sterilised by flaming or passing the article through a gas burner or spirit-lamp flame skin is sterilised by wiping with cotton wool soaked in 70% ethanol solution.
Mathematical requirements
Mathematics is one of the most important basic skills and a subject some learners find tricky. It is important, as many things involve mathematics. The four basic mathematical operations Basic math operations include four basic operations:
- Addition (+)
- Subtraction (-)
- Multiplication (* or x) and
- Division (÷ or /)
In this section, we will briefly perform basic math operations. Take note that, even though the operations and the examples shown here are pretty simple, they provide the foundation for even the most complex operations used in mathematics
 Addition
Addition is when you put two or more objects into a single larger group. The numbers used in the mathematical operation are called the terms, the addends, or the summands. For example, let's say that John has 2 lollipops and Brenda has 4 lollipops, and that we want to find out how many sweets they have together. By adding them together, we see that both of them combined have 6 sweets (2 John's sweets + 4 Brenda's sweets = 6 sweets in total). As you can see, the addition is signified by the 'plus sign (+).
 Properties of addition
There are different properties of addition, such as commutativity and associativity, as well as having an identity element. The identity element is the element in a set of numbers that, when it is used with another number, it leaves that number unchanged.
- For example: number 0 (zero).
- 8 beans+0 = 8 beans
It means that when you add zero to another number, you get that same number as the result. You should also know that if you add physical quantities with units (such as square feet, yards, metres, pounds, kilograms, and so on), they first have to have the same units. It means that you can add millimetres to millimetres but not millimetres to kilograms.
For example: 5 mm + 2 mm = 7 mm, but you cannot add a number with different units. You must convert them first to the same unit.
Subtraction
Subtraction is the opposite of addition. Subtraction is used when you want to know how many objects are left after you take away a certain number of objects from that group. For example, Anna has 4 oranges and she gives 2 oranges to her friend James. How many oranges does she have? She has 2 oranges (4 oranges that she had - 2 oranges that she gave to James = 2 oranges that are left to her). As you can see, subtraction is indicated by the 'minus symbol (-). Subtraction can also be used to pertorm operations with negative numbers, fractions, decimal numbers, functions, and so on. Let us look at an example: 288 - 100 = 188.
Multiplication
Can you remember learning the multiplication tables in the lower grades Learning the multiplication tables help you when multiplying and dividing large numbers. Multiplication of two numbers is equivalent to the addition of a number to itself as many times as the value of the other one number is. Think of it like this: you have 5 groups of apples and each group has 3 apples. One of the ways you can find out how many apples you have is as follows:
3 apples + 3 apples + 3 apples + 3 apples + 3 apples = 15 apples in total
You can see that it is way too much work (especially if you have larger numbers), so you can use multiplication to solve this problem:
5 groups of apples x 3 apples in every group = 15 apples in total
This could be even easier by using the table of multiplication:

Multiplication is signified with the 'multiplication sign (×), and it is often read as 'times' or 'multiplied by'. So if you have an expression like '3 x 4', you could read it as '3 times 4' or '3 multiplied by 4. In other words, the expression of multiplication signifies the number of times one number is multiplied by another number. The number 3 is multiplied in this equation 4 times, and when you multiply 3 by 4 you get the number 12 as a result. The result is called the product.

Division
Division is the fourth basic math operation. It is indicated by the division symbol (÷). You can say that dividing means splitting objects into equal parts or groups. For example, you have 12 apples that need to be shared equally among 4 people. So, how many apples will each person get? Each person will get 3 apples ( 3 apples per person). Division is the opposite of multiplication.
Averages
The average is also referred to as the mean. It involves simple calculations where information related to each other is added together and then divided by the number of sets of information that were added together.
Let us look at an example:
There are five girls in a class aged 15, 13, 18, 12 and 17.
What is the average age of the girls?
15 +13 + 18 + 12 + 17 = 75 (total age) divided by 5 (number of girls)
75/5 =15
The average age is 15 years
 Decimals
The zero and the counting numbers (1, 2, 3,.) make up the set of whole numbers. But not every number is a whole number. Our decimal system lets us write numbers of all types and sizes, using a symbol called the decimal point. As you move right from the decimal point, each place value is divided by 10. The decimal system lets us write numbers as large or as small as we want, using the decimal point. Digits can be placed to the left or right of a decimal point, to show values greater than one or less than one. The decimal point is the most important part of a decimal number. The decimal point will be placed on the line, for example 52.35. Numbers from 1000 to 9999 will be printed without commas or spaces. Numbers greater than or equal to 10000 will be printed without commas. A space will be left between each group of three whole numbers, e.g. 4 256 789.
 Fractions
A fraction represents a part of a whole.
Example: A pizza is divided into six equal parts.
One piece will be referred to as 1 of 6 parts (1/6)
Two pieces will be referred to as 2 of 6 parts (2/6) = 1/3
Three pieces will be referred to as 3 of 6 parts(3/6) = 1/2
All six pieces (the whole pizza) can therefore be represented as 6 of 6 parts (6/6)
When fractions are used, it must always be represented in its simplest form, e.g 3/6 = 1/2.
Look at this record of learners in a primary school who were asked what they had for breakfast:

We can draw this information as a pie chart (like a pizza). To draw a pie chart, we need to represent each part of the data as a proportion of 360, because there are 360 degrees in a circle.
For example, if 55 out of 230 nutrients are bread, we will represent this on the circle
as a segment with an angle of: (55/230) x 360 = 86 degrees. Before you draw the pie chart, 230
remember to check that the angles that you have calculated add up to 360 degrees.
 Percentages
A percentage is a proportion that shows a number as parts per hundred. The symbol '%' means 'per cent'. 9% means 9 out of every 100, or 9/100. Percentages are just one way of expressing numbers that are part of a whole. These numbers can also be written as fractions or decimals. 50% can also be written as a fraction, , or a decimal, 0.5. They are all exactly the same amount. Knowledge of converting between decimals, fractions and percentages is required. Percentage is a value that refers to a part of one hundred expressed in hundredths.A value that is written as 20% is actually 20 of 100 parts (20/100), for example, 50% juice means that 50 of each 100 particles are juice, but the remaining 50 particles are of another type like water and sugar.
 Calculating percentages of amounts
Percentages of amounts can be calculated by writing the percentage as a fraction or decimal and then multiplying it by the amount in question.
Let us look at some examples on how percentages are used:
1. Measurements, such as mass, length and weight, can be converted to percentages
If an apple of 70 g contains 52g of water, the percentage of water in an apple can be calculated as follows
% of water =ᵐᵃˢˢ ᵒᶠ ʷᵃᵗᵉʳ ⁵²ᵍ/ ᵐᵃˢˢ ᵒᶠ ᵃⁿ ᵃᵖᵖˡᵉ ⁷⁰ᵍ﹦ ⁵²ᵍ/⁷⁰ᵍ × ¹⁰⁰ = 74.3%
2. A percentage can be converted to a unit of measurement (mass, weight, length). A bean has a mass of 5 g. If 60% of the bean is water, how much water, in grams, is in the bean?
Mass of water in grams = 5g x ⁶⁰/¹⁰⁰ =3g
Alternatively:
Calculate what 1% of the total weight is: 5 g divided by 100 = 0.05g
If 1% = 0.05 g, then 60% = x 0.05 = 3 g
3. An increase can be expressed as a percentage.
An organism increased in length from 60 to 65 cm. What was the percentage increase?
First, determine the increase in length.
65 cm - 60 cm = 5 cm
Then, use the formula:
% increase = ᶦⁿᶜʳᵉᵃˢᵉ ᶦⁿ ᶜᵐ/ᴼʳᶦᵍᶦⁿᵃˡ ᶦⁿ ᶜᵐ ˣ ¹⁰⁰
⁵ ᶜᵐ/⁶⁰ ᶜᵐ ﹦8.3%
A decrease in (mass, length) can be expressed as a percentage. An organism decreased in mass from 90 g to 35 g. The decrease in mass is thus 55g.
Then, use the formula:
% decrease = ᵒʳᶦᵍᶦⁿᵃˡ ᶦⁿ ᵍ/ ᵒʳᶦᵍᶦⁿᵃˡ ᵐᵃˢˢ ˣ ¹⁰⁰
⁵⁵ ᵍ/ ⁹⁰ ᵍ ˣ ¹⁰⁰ ﹦ 61.1%
4. Convert a % increase to an increase in measurement (length, mass).
The length of an organism increased by 60% from its onginal length of 50 cm. What was its final length?
First, determine the increase in length.
Use the formula: gain in lenath = onginal length in cm / 100 x increase in %
Gain in length = 60/ 100 × 50 cm = 30 cm
Then, it the original length was 50 cm and the organism gained 30 cm in length, then the final length is:
50 cm + 30 cm = 80 cm
5. Find the original measurement (mass, length) of an organism after it has lost a percentage of its mass. An organism lost 30% of its mass and ends up with a final mass of 85 g. What was the original mass?
First, find the final mass as a percentage of the original mass.
The original mass was 100%, so subtract 30 (mass lost) from 100% and the result is 70%.
Use the formula:
Original mass in grams = final mass in g / 70 × 100 = ?
85 g / 70 × 100 = 121.4 g
 Ratio
A ratio is the relation between two quantities expressed in a numerical form. The ratio indicates how many times bigger or smaller one thing is compared to another. Ratios are calculated by dividing the smallest number into the largest number. For example, a biologist investigated the flowers of a specific plant. She divided them into red and purple flowers. She discovered that there were 150 purple flowers and 50 red flowers. The ratio of purple flowers to red flowers = 150:50 = 3:1 Ratios are used to show how things are shared. For example, the necklace in the image has a pattern of two red beads for every three yellow beads. The ratio of red beads to yellow beads is 2:3. Ratios Can have more than two numbers, for example, 3:4:2.
Reciprocal
A reciprocal is an inverse of a number, which means a fraction that is turned around. The reciprocal of 2 (2/1) is 1/2 ; 2 (1/2) 5/2 is 2/5, and so on.
Any number multiplied by its reciprocal is always 1.
For example: 3/4 × 4/3 = 1
Mathematical instruments (ruler, compasses, protractor, set square)
 Ruler
The ruler is a tool used to rule straight lines and measure distances. Usually a ruler is marked in cm along the top and mm along the bottom. You can use a ruler to join the points in a graph, draw a table or draw a label line to label a diagram.
Compasses
A pair of compasses, also known simply as a compass, is a technical drawing instrument that can be used for drawing circles or arcs. As dividers, they can be used as tools to measure distances, in particular on maps. Compasses can be used for mathematics, drafting, navigation and other purposes.
 Protractor
A protractor helps you measure angles in degrees. Protractors usually have two sets of numbers going in opposite directions. Be careful which one you use! When in doubt, think 'should this angle be bigger or smaller than 90°?
 Set square
A set square or triangle (American English) is an object used in engineering and technical drawing, with the aim of providing a straight edge at a right angle or other particular planar angle to a baseline.
Direct and inverse proportion
Direct proportion
There is a direct proportion between two values when one is a multiple of the other. For example, 1 cm = 10 mm. To convert cm to mm, the multiplier is always 10. Direct proportion is used to calculate the cost of petrol or exchange rates of foreign money. The statement 't is directly proportional to r' can be written using the proportionality symbol:
t * r
If y = 2p, then y is proportional to p and y can be calculated for p = 7
y= 2 x 7 = 14
Similarly, if y = 60, then p can be calculated:
60 = 2p
To find p, divide 60 by 2:
60 ÷ 2 = 30
When we discuss the factors that affect the rate of photosynthesis, you will see they are directly proportional-when light intensity increases, the rate of photosynthesis increases.
 Inverse proportion
If one value is inversely proportional to another, then it is written using the proportionality symbol a in a different way. Inverse proportion occurs when one value increases and the other decreases. For example, more workers on a job would reduce the time to complete the task. They are inversely proportional.
The statement *'b* is inversely proportional to *m'* is written: *b x 1/m*
Equations involving inverse proportions can be used to calculate other values.
Using: g = 36/ (so g is inversely proportional to *w*")
If g = 8, then find *w*:
*w* = 36/w
Similarly, if *w* = 6, find g:
g= 36/6
g= 6
For example, when the temperature increases beyond the optimum temperature, the rate of enzyme activity decreases.
Positive, whole number indices in algebraic
expressions
Indices refer to the sequential arrangement of numbers. In order to understand and use indices, you must first understand the basic principles of squared numbers, cubed numbers, and their roots. A squared number is displayed as 4. This means that the number 4 is squared, or 4 x 4. The small 2 is referred to as an index number, or power. It is this small number that tells you how many times you must multiply the main value (in this case 4) by itself. This series of numbers are known as square numbers. These are the values that you get when you multiply an integer by itself. For example, the first 5 square numbers are as follows:
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
The opposite of a square number is a square root. The square root of a number is often denoted by the symbol V¯¯¯¯.
 Whole numbers
Whole numbers are simply the numbers 0, 1, 2, 3, 4, 5, ... (and so on), in other words, no tractions.

|￣|￣|￣|￣|￣|￣|￣|￣|￣|￣|
0  1   2  3   4   5  6   7   8  9   10

Examples: 0, 7, 212 and 1023 are all whole numbers.
 Solving equations
X and y are called variables. This is because they are not identified with speatic numbes yet, and so they represent a whole range of different numbers. Therefore, they vary, in Other words, variables are placeholders tor numbers.
The terms -5xy and yx are like terms. Both consist of the same vaniables, meaning that you can add and subtract like terms. Solve the following equation for x. The first thing to do is to move away the numbers that are not in the same term as x. the 2 is part of the same term as x. 2 and x are closer to each other (they are part of the same term), and so we should move the 3 being added to it is a different term. The 2 is part of the same term as x. In this sense  2x + 3 = 15 away the numbers that are not in the same term as x the are part of the same term), and so we should move the 3 away first. 2x + 3 - 3 = 15 we subtracted 3 from the left-hand side of the equation. But we know that we do the same operation to both sides, to preserve the equation.
So we take away 3 from both sides:
2 x + 3 - 3 = 15 - 3
This gives us: 2x = 12
It should be clear now that the answer is 6. However, we still need to complete our method, So that we can complete harder problems later on.
2x = 12
We divide both sides by 2 to get:
2x/2 = 12/2
If you look at the left-hand side of the above equation, you can see that x is being multiplied by 2, and then divided by 2. But doubling a number and then halving it gets you back to where you started.
The left-hand side is just x.
Our equation is: X = 12/2
We know that 12 divided by 2 is 6. We end up with: X = 6.
Planning and conducting investigations
Planning
During summer, learners noticed that butterflies visit brightly coloured flowers. The dull flowers, such as grass, do not attract butterflies. The learners must explain why this occurs and think of possible answers to their observation. The problem to be investigated (why buttertlies visit brightly coloured tlowers but not dull flowers) is first defined, bearing in mind the time and resources available. It is easy to initially overestimate what can be achieved, and to set yourself a demanding schedule. Using your knowledge and experience, and with the guidance of a teacher, or with a group of learners, discuss your ideas in detail to ensure that the experimental procedure can be carried out safely and effectively. Consider, too, the ethical implications of your approach, such as the involvement of living organisms and possible environmental consequences. This process is referred to as planning. Learners wanted to know if their observation had to do with bright colour or if there were other tactors that played a role and why. This will lead them to what is called a hypothesis. To test a hypothesis, you have to come up with a prediction with which you can test the experiment. Let us say the learners wanted to investigate the reasons why buttertlies visited the brightily coloured flowers and not the dull flowers. They will need to carry out what is called a sCien tific experiment. First, they will need to identity the variables that they are going to use in their experiment. One variable will be a control and another variable will measure the dependent variable.
 Implementing plans
An important step is the design of a record sheet, as this requires you to be dear about exactly what data you have to obtain and when.

 Hypothesis (in relation to dependent and independent variables)
A hypothesis is an idea or belief about something that can be proved. Many scientists try to prove their hypothesis by doing an experiment. For example, if you had an idea or hypothesis that ammonia diffuses more rapidly at high temperatures than at low temperatures, you would need to design an experiment to investigate your hypothesis. Whenever you design an experiment, you must be sure that it is a fair test. You must be sure that everything is kept exactly the same, apart from the one thing that you are investigating. In this case, it IS the temperature. You must keep the following exactly the same:
- position of the litmus paper
- the size of the cotton wool
- the length of time the cotton wool is held in the ammonia solution.
The only thing that can be different is the temperature. If you find any differences in your two sets of results, you will know that it must have been the temperature that made the difference! In your notebook, try designing a new experiment to investigate your hypothesis.
 Testing a hypothesis
A hypothesis comes about as a result of observations being related to a theory. To test a hypothesis, you need to design a fair test where you isolate the factor influencing the hypothesis, in this case temperature, and repeat the experiment keeping everything else exactly the same (constant). The thing that changes is described as the variable. The only variable is temperature. The sequence of stages in testing a hypothesis is as follows:
- State your hypothesis.
- Describe your method.
- Carry out the experiment.
- Record your observations.
- Explain your results.
- Do the results support your hypothesis?
- If not, revise your original hypothesis.
 Variables
In an investigation or experiment, the specific conditions are called variables. Most of the variables are deliberately kept the same, but others vary. In fact, there are really three types of variables. We can demonstrate them by referring to an example experiment, such as the investigation of the rate of an enzyme-catalysed reaction shown below.

The variables that are always kept the same in this investigation of the rate of reaction of catalyse are the conditions, such as temperature, the volumes and concentration of the reagents, and the pH. Variables that are kept constant are called controlled variables. In Figure abive, you can see that the rate of reaction is measured at 30-second intervals. The times that readings are taken is the variable that is manipulated by the experimenter, and this is called the independent variable. Note that it has been recorded in the table as a list, before the experiment was started. In the experiment, the amount of oxygen that has collected at 30-second intervals is the variable accurately measured by the experimenter It is called the dependent variable. This is recorded in the second column of the table. As a matter of interest, it would be equally possible for the experimenter to have recorded the time taken for 20 cm of oxygen to collect. In this case, which is the independent variable and which is the dependent variable? Experimental investigation is concerned with observing changes or variable properties of substances. These variables are of two main kinds:
- Qualitative variables cannot be measured by simple means and the information Collected is not numerical. It includes colour, smell, taste, temperature and moisture. These variables can only be collected by observation.
- Quantitative variables can be measured as numbers, length, mass, heat energy, pressure or time.
 Recording data
Data reters to a collection of facts from which conclusions may be drawn - statistical data.
 Types of data
In practicals and investigations, observations are recorded as data. There are different forms of data, but they are all potentially useful. No one type that is relevant to your enquiry is superior to another, providing they have been accurately taken and recorded. We define the data that we collect as:
- qualitative observations, for example in behaviour studies, such as the feeding mechanism of honey bees visiting flowers, or the nesting behaviour of a species of bird. Qualitative data may be recorded in written obsenvations or notes, or by photography or in drawings.
- quantitative observations, for example the size (length, breadth or area) of organs, such as the leaves of a plant in shaded and exposed positions, or pH values of soil samples in different positions.
Recording data
When you plan an investigation or experiment, think carefully about the data you expect to Collect. This allows you to prepare a record sheet with spaces for the information, both qualitative and quantitative. Design a table for the numerical data. This table should indicate how often you must record the data, as well as exactly what will be recorded.
 Displaying data
First, you must select from the data what is important. For example, it may be appropriate to round up numbers to fewer figures, in order to avoid giving aata a greater level of accuracy than the measurements warrant. Then, display the important data, using a visual summary, making their importance clear. This may involve using one or more graphs or tables.
 Drawing graphs and tables
Tables
- Each column of a table will be headed with the physical quantity and the appropriate unit, for example, time/s.
- There are three acceptable methods of stating units, for example, metre per second or m per s or m s-¹.
- The column headings of the table can then be directly transferred to the axes of a constructed graph.
- The table should be enclosed with a border.
How to draw a graph
A graph is a diagram showing the relationship between variable quantities, usually of two variables, each measured along one of a pair of axes at right angles. The independent variable is the quantity whose values are chosen by the experimenter, such as distance in metres and time in seconds. This variable is always on the horizontal axis. This axis is described as the x-axis.

The dependent variable is the quantity that is being measured, such as the number of bubbles released and time taken to move a certain distance. This variable is always on the vertical axis. This axis is described as the y-axis. When you draw a graph, make sure that you do the following:
● Unless instructed otherwise, the independent variable should be plotted on the x-axis (horizontal axis) and the dependent variable plotted on the y-axis (vertical axis). Decide which activity will be plotted on the X-axis, as shown in Figure above This is always the activity that is fixed by the experimenter. In this case, it is the distance at which the red litmus paper is attached to the tube. So, distance will be plotted on the horizontal or X-axis. The other activity, the time taken for the paper to turn blue, is plotted on the vertical or y-axis.
● Each axis should be labelled with the physical quantity and the appropriate unit, for example, time/s.
● Unless instructed otherwise, the scales for the axes should allow more than half of the graph grid to be used in both directions, and be based on sensible ratio5, for example, 2 cm on the graph grid representing 1, 2 or 5 units of the variable. In this case, it is 0 and 50. We need a scale that will go from 0 to 50 in equal intervals. Do the same for the vertical axis. In this case, it is 0 to 20.
● Let your curve use as much of the graph paper as possible, at least 50% of the grid.
● The graph is the whole diagrammatic presentation, including the best-fit line when appropriate. It may have one or more sets of data plotted on it.
● Points on the graph should be clearly marked as crosses (x) or encircled dots (•).
● Plot each point with a small cross, x. If you have two sets of data to plot on the same axes, use an encircled dot (•) or a vertical cross (x).
● Large 'dots' are penalised. Each data point should be plotted to an accuracy of better than one half of each of the smallest squares on the grid.
● A best-fit line (trend line) should be a single, thin, smooth straight line or curve. The line does not need to coincide exactly with any of the points; where there is scatter evident in the data, examiners would expect a roughly even distribution of points either side of the line over its entire length. Points that are clearly out of the normal range should be ignored when drawing the best-fit line.
● Join each point in turn using a ruler. No extrapolation (a line extended toward a point or away from the point). It should be point to point.
● Always mark your points and draw the graph line (this is always called a curve, even if it is a straight line!) with a sharp pencil.
● Finally, give your graph a heading. In this case, it could be: Graph showing the relationship between distance of litmus paper from end of tube and the time taken for the paper to turn blue'.
Sometimes you will need to use the omission sign(//) and a zero to scale properly.

 Bar charts
Bar charts are used with discrete data to show relative proportions. There should be small gaps between the bars of equal width and the bars should be presented in order of magnitude. Bars do not touch. Bars must be labelled in the centre of a bar, underneath the x-axis. The height of each bar gives the frequency and one of the variables might not be numerical. Bars should be arranged from most to least and must cover at least 50% of the graph paper on the x- and y-axis.

 Histograms
Histograms are useful with continuous data, and the data can be arranged in classes. The bars touch each other to show continuity and are of equal width, and the height and area of each bar must match the proportion of the data. To draw a histogram, you will need a piece of graph paper, a ruler and a pencil. However, you need to have the data in a table first. Histograms are drawn when plotting frequency graphs with continuous data, for example, frequency of occurrence of leaves of different lengths. The blocks should be drawn in order of increasing or decreasing magnitude and they should be touching. Figure below is an example of a histogram.

 Pie charts
Pie charts are best used for showing relative proportions. These should be drawn with the sectors in rank order, largest first, and beginning at 'noon and proceeding clockwise. Pie charts should preferably contain no more than six sectors.

Column graphs
These are drawn when plotting frequency graphs from discrete data, for example, frequency of occurrence of leaves, with different numbers of prickles or pods, with different numbers of seeds. They should be made up of narrow blocks of equal width that do not touch.
 Interpretation of graphs and charts
When you provide a written description of a graph, it should be done in such a way that whoever is reading the description will be able to see a picture without looking at the graph. For example: Warm-blooded animals need to maintain a constant internal temperature. In cold weather, some of these animals crowd closely together in a group. To investigate the advantages of crowding together in such a group, a learner followed the drop in temperature of 10 cm of water in a test-tube. Test-tube A was used to represent a single animal, as shown in Figure below.

Test-tubes B and C were used to represent part of a crowded group of animals, using seven test-tubes, as shown in Figure below.

The temperature of the tubes labelled A, B and C was measured, using a thermometer, every 2 minutes for 10 minutes. All test-tubes had 10 cm? of water with the same starting temperature of 55 °C. The results are shown in Table below.

A graph of the results was plotted to clearly show the difference between the three sets of data.

● Describe the results of test-tube A: Two stages should be identified (reference can be made to the loss of heat, or to the change in temperature, for example, more heat was lost at 12 °C during the first 2 minutes, then less heat was lost during the next 8 minutes, or the temperature dropped faster at first and then slowed).
● Describe the difference between the results for test tube A and those for test-tubes B and C: It must be possible to identify the position of all three sets of data, and relate it to the speed of the reaction. Compare A to B and C: for example, the water in A lost more heat than C, while C lost more than B. Or the water in A lost most heat then C and B. Or the water in C lost more than B, but less than A.

 The End, Posted by Miss Fang Xiu.