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Quality of Measurement Coursework Booklet

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Quality of Measurement Coursework Booklet Powered By Docstoc
					      Walton High



      AS Quality of
      Measurement Task
      Physics in Practice Coursework Booklet
      Dr. S. Harding.




                                 2009-2010


Quality of Measurement Task                    Page 1
Contents

  Contents ........................................................................................................................................... 2
  Introduction ...................................................................................................................................... 3
  What are the aims? ........................................................................................................................... 5
  Things for You to do ........................................................................................................................ 6
  Quality of Measurement tips ............................................................................................................ 7
     Pre-lim .......................................................................................................................................... 7
     Gathering data .............................................................................................................................. 7
     Analysis ........................................................................................................................................ 7
     Writing Up ................................................................................................................................... 7
     Marking ........................................................................................................................................ 8
  Suggested Tasks ............................................................................................................................... 9
  Advancing Physics – Quality of Measurement Planning Sheet ..................................................... 10
  Strands of assessment in the Quality of Measurement task ........................................................... 12
  Making sense of data coursework - practice. ................................................................................. 14
  Why do I want to use Excel, anyway? ........................................................................................... 15
     How do I open Excel? ................................................................................................................ 15
     How do I save my work? ........................................................................................................... 15
     How do I put data into my sheet? .............................................................................................. 15
     How do I get it to calculate stuff for me? .................................................................................. 16
     What is the 'Nifty Short Cut' for copying a formula down a column? ....................................... 17
     How do I use Excels built in formulae? ..................................................................................... 17
     How do I do graphs? .................................................................................................................. 18
     How do I change it so it plots V against I or P against I? .......................................................... 19
     Hmm. Is there a less fiddly way? .............................................................................................. 20
     Let's get fancy… ........................................................................................................................ 21




Quality of Measurement Task                                                                                                                   Page 2
Introduction
As part of your quality of measurement coursework you will be required to devise an approach to
an experiment and then carry it out and perform some careful data analysis of your results.

There are many ways to tackle a problem (some better than others) as the following story illustrates:


The following is a question on a physics exam at the University of Copenhagen:

       "Describe how to determine the height of a skyscraper with a barometer."

       One student replied: "You tie a long piece of string to the neck of the barometer, then
       lower the barometer from the roof of the skyscraper to the ground. The length of the
       string plus the length of the barometer will equal the height of the building."

       This highly original answer so incensed the examiner that he failed the student who
       immediately appealed on the grounds that his answer was indisputably correct.

       The university appointed an independent arbiter to decide the case.

       The arbiter ruled that the answer was indeed correct, but did not display any noticeable
       knowledge of physics. It was decided to call the student in and allow him six minutes in
       which to provide a verbal answer which showed at least a minimal familiarity with the
       basic principles of physics.

       For five minutes the student sat in silence, forehead creased in thought. The arbiter
       reminded him that time was running out, to which the student replied that he had
       several extremely relevant answers, but couldn't make up his mind which to use.

       On being advised to hurry up the student replied: "First, you could take the barometer
       up to the roof of the skyscraper, drop it over the edge, and measure the time it takes
       to reach the ground. The height of the building can then be worked out from this
       formula I have worked out for you on my text paper here."

       Then the student added, "But, Sir, I wouldn't recommend it. Bad luck on the
       barometer."

       "Another alternative", offered the student, "is this: If the sun is shining you could
       measure the height of the barometer, then set it on end and measure the length of its
       shadow. Then you measure the length of the skyscraper's shadow, and thereafter it is a
       simple matter of proportional geometry to work out the height of the skyscraper. On
       the paper is the formula for that as well."

       "But, Sir, if you wanted to be highly scientific about it, you could tie a short piece of
       string to the barometer and swing it like a pendulum, first at ground level and then on
       the roof of the skyscraper. The height is worked out by the difference in a gravitational
       formula, which I have determined here this time on a long sheet of paper with a very
       long and complicated calculation."

       "Or, Sir, here's another way, and not a bad one at all. If the skyscraper has an outside
       emergency staircase, it would be easier to walk up it and mark off the height of the
       skyscraper in barometer lengths, then add them up."

       "But if you merely wanted to be very boring and very orthodox about the answer you
       seem to seek, of course, you could use the barometer to measure the air pressure on
       the roof, and on the ground, and then convert the difference in millibars into feet to
       give the height of the building."

Quality of Measurement Task                                                                   Page 3
      "But since we are constantly being exhorted to exercise independence of mind and
      apply scientific methods, undoubtedly the best way would be to knock on the janitor's
      door and say to him 'If you would like a nice new barometer, I will give you this one if
      you tell me the height of this skyscraper'."

      The student was Niels Bohr, the only Dane ever to win the Nobel Prize in physics.




              Niels Henrik David Bohr (1885-1962)
              Danish physicist and one of the foremost scientists in modern physics. He was
              professor of theoretical physics at the University of Copenhagen and was later
              director of its Institute for Theoretical Physics, which he helped to found. He
              was awarded the Nobel Prize in 1922 for his work on atomic structure and the
              hydrogen atom. Classical theory had been unable to explain the stability of the
              nuclear model of the atom, but Bohr solved the problem by postulating that
              electrons move in restricted orbits around the atom's nucleus and explaining
              how the atom emits and absorbs energy. He thus combined the quantum
              theory with this concept of atomic structure. He was also known for his robust
              jousts, often humorous with Albert Einstein.




Quality of Measurement Task                                                               Page 4
What are the aims?
Candidates should develop a sense of pride in measuring as well as possible given the tools they have, and to
be clear about how well the job has been done. They should be able to experiment well, to recognise the
limitations of instruments and to discuss the uncertainty of measurements, learning to look for important
sources of uncertainty and attempt to reduce them. They should also consider possible systematic errors and
try to remove them. Candidates should be able to analyse data carefully make intelligent use of graphs and
tables, extract as much information as possible and present a report that explains clearly the procedures they
have used. The written record should communicate the results obtained and have a clear outcome that is
qualified with statements of uncertainty.

Quality of Measurement

Candidates undertake a task of the following kind:

    • a careful measurement of a physical quantity;
    • a careful quantitative study of the relationship between two or more variables, where there are
        some indications from theory of what to expect;
    • a careful calibration of a sensor or instrument;
    • a careful study of one or more of the properties of a sensor or instrument;
    • a comparison of methods of measuring the same thing.



The word ‘careful’ implies both practical skill (‘hands on’) and thoughtful analysis of problems and
data (‘minds on’).

Candidates should demonstrate their ability to:

    • recognise the qualities and limitations of measuring instruments, particularly resolution,
        sensitivity, calibration, response time, stability and zero error;
    • identify and estimate the most important source of uncertainty in a measurement and seek
        ways to reduce it;
    • consider the possibility of systematic errors and seek to estimate and remove them, including
        considering calibration;
    • make effective plots to display relationships between measured quantities, with appropriate
        indication of uncertainty;
    • use simple plots of the distribution of measured values to estimate the median (or mean)
        value and the spread (which may be estimated from the range of values), and to identify
        and account for outlying values.


A written report of the work done is produced. This task builds on the measurement tasks
that candidates will have performed in their experimental work throughout the AS course.



Quality of Measurement Task                                                                           Page 5
Things for You to do

   1. Have a go at the practice task near the end of this booklet
   2. Choose a task for your investigation.
   3. Check with us that it is possible.
   4. It is up to you to work out how you will undertake your task and what equipment you will
      need so some research is vital – use the web, books journals etc.
   5. Produce a plan using the sheet provided and get it signed off by us
   6. Create a detailed equipment list – you must list EVERYTHING that you will need including
      quantities so the lab technicians can prepare it. If you don’t list it you won’t get it
   7. Read the textbook and this booklet very carefully so you know how to handle uncertainties
      and errors – this is essential for high marks. You need to gather enough data to estimate
      the uncertainties in your measurements
   8. If you have a laptop bring it in for the practical’s – record data as you go and use excel to
      plot graphs and check the quality of your results. Or plot by hand. It will be too late to redo
      things if you find out later that your data is junk
   9. Read the mark scheme in this guide very carefully so you know what you need to do to
      access the marks
   10. There will be NO chance to redraft – once you hand in that’s it.




Quality of Measurement Task                                                                     Page 6
Quality of Measurement tips


Pre-lim

Before you start the practical work know exactly what you are trying to achieve. Do not turn up to the lab
unless you can fully answer the following questions:

    1.   How do I set things up?
    2.   What exactly do I need to measure?
    3.   How am I going to minimize/reduce errors
    4.   How many results do I need (aim for at least 10 repeats)
    5.   What is the background theory

With regard to error – think carefully about how to reduce them. For example a measuring the diameter of a
wire with a micrometer is good, but would it be better to calculate it using density and volume information?

Your pre-lim should allow you to identify problems and sources of error then IMPROVE your final method.
YOU GET MARKS FOR THIS


Gathering data

Everything comes from your data, you must make sure you obtain enough results for meaningful analysis –
one or two runs is NOT enough. How much data you need will depend on your topic, for example

    1. Measuring the resistivity of wire – record data for 10 different lengths of wire then repeat with 2 new
       pieces of wire. This will give you 30 sets of results
    2. Youngs Modulus – record stress and strain 10 times, then repeat using 2 new wires. This will give
       you 30 results BUT only 3 Youngs Moduli since you must use all 10 results to calculate the modulus

Plot your data as you go – it is too late to discover your data is junk after the practical work has Finished


Analysis

You need to process your data and draw meaningful graphs with error bars. Read page 51 onwards in the
textbook very carefully. Essentially, work out means for your data then look at the spread either side of the
mean i.e. the max-min range. It is this range that will define your error bars.

To discuss accuracy compare you results to expected values if you can, For example you can lookup the true
values of Young’s modulus or resistivity in databooks – how close are your results to this?


Writing Up

Imagine you are writing for someone who knows no physics. You should be able to give your report to a
complete novice who can then follow your instructions, carry out the experiment and get the same results
that you did.

Read the marking section below and as a rough guide use the following structure:

The underlined red words should be sub-headings in your report.

    1.       Statement of the problem and what you intend to do.


Quality of Measurement Task                                                                               Page 7
   2.      The method of obtaining results, including the properties of the sensor/measuring
           instrument and any calibration.
   3.      The background physics of the experiment.
   4.      Results: repeats, units, well-chosen tables, tolerances.
   5.      A statement on how you took steps to reduce uncertainty.
   6.      Graphs, showing errors. These MUST include error bars.
   7.      The biggest source of UNCERTAINTY, with an estimate.
   8.      A discussion on ANOMALIES and systematic errors.
   9.      Cross-checking of results, using alternative ways of looking at the data.
   10.     A clear outcome, qualified with a statement about errors.
   11.     Possible improvements to the method. (you should have tried these out.)



Marking

There are four strands to the assessment of this piece of work, YOUR REPORT MUST ADDRESS ALL
THESE STRANDS:

   1. Quality of the practical work in the laboratory
   2. Quality of thought about uncertainty and systematic error, and attempts to improve the
      measurements
   3. Quality of communication of physics in the report
   4. Quality of handling and analysis of data




Quality of Measurement Task                                                                    Page 8
Suggested Tasks


You will be assigned one of the following tasks – everybody will do something different.


   1. A careful measurement of a physical quality - For these experiments you should
      measure it then improve your method and measure it again more accurately

          • Breaking stress of a wire – 5 sets of equipment available
          • Conductivity of copper - 5 sets of equipment available
          • Gravitational field strength near the Earth’s surface - 5 sets of equipment available
          • Power and/or magnification of a lens of a lens - 5 sets of equipment available
          • Speed of sound in air - 1 set of equipment available
          • Youngs modulus of copper - 5 sets of equipment available

2. A careful quantitative study of the relationship between two or more variables, where
       there are some indications from theory of what to expect

          • Absorption of light with thickness of materials, or concentration of a solution - 2 sets of
          equipment available
          • Resistance of a metal wire and temperature - 1 set of equipment available
          • Response of a solar cell to varying light intensity - 5 sets of equipment available
          • Speed of a trolley down a slope and angle - 2 sets of equipment available
          • Speed of falling paper cones and area - 5 sets of equipment available

3. A careful calibration of a sensor or instrument

          • LDR used as a simple light meter - 3 sets of equipment available
          • Rotary potentiometer as an angle sensor - 2 sets of equipment available
          • Thermistor used as a simple thermometer - 2 sets of equipment available

4. A careful study of one or more of the properties of a sensor or instrument

          • Response time of a thermistor - 2 sets of equipment available
          • Sensitivity of a thermistor - 2 sets of equipment available

5. A comparison of methods of measuring the same thing

          • Liquid level based on flotation and a rotary potentiometer compared with an LDR and
              light source - 1 sets of equipment available
          • Measuring “g” in more than one way - 1 set of equipment available
          • Proximity using an ultrasonic sensor compared with another method – 1 set of
          equipment available




Quality of Measurement Task                                                                       Page 9
Advancing Physics – Quality of Measurement Planning Sheet

Name _________________________________________         Teacher ________________________

Dates of practical work ______________________ Hand in the report by: ________________


Proposed title of my project



What I am trying to measure or achieve




Background Physics – Equations and theory




Outline of my plan and method




Outline of possible sources of uncertainty and ways of reducing uncertainties




Quality of Measurement Task                                                     Page 10
Equipment List with a justification for its use compared to alternatives and information
about ± errors or uncertainties


Item + Quantity               Justification                                   ± error




Safety Issues I need to think about (Compulsory)




Teacher’s comments




Quality of Measurement Task                                                        Page 11
Strands of assessment in the Quality of Measurement task
1. Quality of practical work in the laboratory

Was the practical work done systematically and carefully, showing skill in handling and using apparatus?
Were sufficient observations and measurements made to deal with the problem? Were results tabulated
carefully in a well-thought-out structure, recorded as they were taken? Were measurements made so as to
minimise systematic error, and to reduce uncertainty to the limits allowed by the apparatus?

 Level 1                                                     Methods and approach have limitations, with
                                                             shortcomings in the measurements and
                                                             observations and limited attention to
                                                             practical detail.
 Level 3                                                     Methods and approach are adequate, with
                                                             relevant measurements and observations
                                                             and competent attention to practical detail.
 Level 5                                                     Methods and approach are well chosen, with
                                                             sufficient measurements and observations
                                                             made to deal with the problem and
                                                             considerable skill used to obtain them,
                                                             avoiding unnecessary systematic error.

2. Quality of thought about uncertainty and systematic error, and attempts to improve the
       measurements

Were the relevant properties of sensors or measuring instruments studied and assessed
systematically and carefully? Was the calibration of instruments considered, and
attempted where possible? Was the largest source of uncertainty identified and estimated?
Were possible systematic errors considered, and their sign identified? Did the student
suggest and try out possible improvements to the experimental method and apparatus used?

 Level 1                                                      Measuring instruments are used directly
                                                              without consideration of their properties; little
                                                              understanding of the nature of error or
                                                              uncertainty is shown, and data is limited to a
                                                              simple set of measurements.
 Level 3                                                      Some efforts are made to use measuring
                                                              instruments to their best advantage; error and
                                                              uncertainty are considered, possibly with
                                                              some flaws in approach, and some
                                                              improvements to experimental method are
                                                              considered.
 Level 5                                                      The relevant properties of measuring
                                                              instruments are assessed systematically;
                                                              errors and uncertainty are identified and,
                                                              where possible, reduced and improvements
                                                              to the experiment to reduce error and
                                                              uncertainty are tried out.




Quality of Measurement Task                                                                    Page 12
3. Quality of communication of physics in the report

Is the report clear, well-ordered and concise, with enough detail to allow someone else to repeat
the experiment and obtain similar measurements? Does the report explain clearly the physics of
the experiment? Was available ICT used well? Are graphs and tables well-chosen, and presented
so as to communicate the findings as well as possible? Is the use of English effective for the
purpose?

 Level 1                                                  Recording and presentation of data lacks
                                                          clarity; graphical plots may be inappropriate
                                                          or incorrect and the report is poorly
                                                          structured and presented.
 Level 3                                                  Data are presented clearly, with some
                                                          possible inconsistencies in headings, units or
                                                          significant figures; graphical plots are clear
                                                          and the report covers most details needed to
                                                          repeat the experiment.
 Level 5                                                  Data are presented clearly and effectively
                                                          with correct headings, units, tolerances and
                                                          significant figures; graphical plots are well
                                                          chosen to display the data to good effect and
                                                          the report is clear, concise, well-structured
                                                          and gives all details needed for someone
                                                          else to repeat the work.


4. Quality of handling and analysis of data

Was data analysed with care and attention, looking for anomalies or unexpected features, and
extracting as much information as possible? Does the analysis demonstrate a clear and correct
understanding of the physics involved? Were results cross-checked through alternative ways of
looking at the data or going back to the apparatus? Was there a clear claim about the outcome,
qualified with statements of uncertainty and possible systematic error?

 Level 1                                                  Analysis is limited to direct calculations or
                                                          plots of measured data with possible major
                                                          flaws in physics, or no attempt to explain the
                                                          outcomes in terms of physical ideas, and
                                                          limited attempt to discuss shortcomings in
                                                          procedures.
 Level 3                                                  Some correct calculations of relevant
                                                          quantities are made with an attempt to
                                                          discuss the outcomes in terms of physical
                                                          explanations (including discussion of errors
                                                          and uncertainties) with minor errors of
                                                          physics in the analysis. Obvious anomalies
                                                          are noted.
 Level 5                                                  Data are analysed carefully, extracting as
                                                          much information as possible, leading to a
                                                          clear claim about the outcome, well-founded
                                                          in the data and analysis, demonstrating
                                                          understanding of the physics and relating
                                                          uncertainties in the conclusions to limitations
                                                          of the procedures and the measurements
                                                          made.




Quality of Measurement Task                                                                Page 13
Making sense of data coursework – practice task.

Below are the results of an experiment about the time period of a pendulum.

    Length (m)            Time
                            (s)
       0.02               0.284
       0.04               0.401
       0.06               0.491
       0.08               0.567
       0.10               0.634
       0.12               0.695
       0.14               0.750
       0.16               0.802
       0.18               0.851
       0.20               0.897
       0.22               0.940
       0.24               0.982
       0.26                1.02
       0.28                1.06
       0.30                1.09

1. Type these results into Excel and produce a graph with length along the bottom and time up
   the side. Use the 'Simple Graphs' section of the Bluffer's Guide. Print.

2. The theory of the simple pendulum is that the time for one oscillation
                 l
      T  2
                 g

    To see if the experimental results agree with the theory you need to process them to find a
    straight line graph. If the equation above is correct then a graph of T against l will be a
    straight line through (0,0).

    To do this, make another column on the spreadsheet for length. Use a calculator or an
    equation in Excel to calculate the square root of each of the lengths. [The equation is =(cell
    with length in it)^0.5]. Print the sheet.

3. Now plot the graph of time against length. You may need to move the columns about to get it
   with time up the side. Print.

4. Use the 10 steps sheet to make it look more professional. Print.

5. You should have a trendline that is of the form y=mx. According to the theory
                     2
              T          l
                      g
    is like   y=m         x                  so the gradient of the line m = 2/g
                                             so, rearranging,             mg = 2
                                                            g = 2
                                                                                 m
                                                                             g = 4
                                                                                 m2
    Find m from your trendline equation.
    Create a bubble from Autoshapes, copy the equation for g into it and work out a value for g.
It should be 9.81N/kg. Comment on the value that you got and write it in the bubble. Print

Quality of Measurement Task                                                                  Page 14
Why do I want to use Excel, anyway?

You really do want to use Excel when you have data and you want to calculate things or
make graphs, which pretty much means whenever we do experiments with even a small
amount of data.

Please remember that this program was written for business, not science, and that it has
no brain. YOU are the one with the grey matter and 'garbage in, garbage out' applies.
Always think 'Does that look reasonable?' first, before trusting it or printing it out.

How do I open Excel?
Open Excel using the Start menu, then Programs then Microsoft Excel (or Microsoft Office then
Microsoft Excel).
You will get this (depending on the version):

                                                          Chart wizard




     This is cell A1                  Formula bar                        Increase decimal
     - all cells have                                                    places button
     a reference                                                         (decrease is the
                                                                         next one)




         This is sheet 1 - you can
         have lots of sheet in each
         workbook




How do I save my work?
From the File menu, click Save As, type a file name for the workbook. Click Save.


How do I put data into my sheet?
You make tables in Excel just like the ones that you would draw for data when doing your
experiment.
Let's imagine that you have the following data for a resistor - type it into Excel so it looks
like this:

Quality of Measurement Task                                                                 Page 15
 Voltage (V)             Current (A)
 0.0                     0.00
 2.0                     0.51
 4.0                     0.98
 6.0                     1.40
 8.0                     2.07
 10.0                    2.55
 12.0                    3.00

You should notice that the numbers change so that 0.00 changes to 0. You can change this back by
highlighting the column and then pressing the 'increase decimal place' button.


How do I get it to calculate stuff for me?

Type 'Resistance' in the heading of the next column. [Check out the 'Let's get fancy' section at the
end to work out how to put () in as well]

Click on cell C2 (underneath where you have typed resistance) and then press the = sign on the left
of the formula bar. Then click on cell A2, then / on the keyboard then on cell B2 so that it looks
like this:




Click OK and you will get a nasty looking thing that says: #/DIV/0! That's because it doesn't like
dividing by zero, and neither should you. We'll let it ride for now.
We want to find out the resistance for the other pairs of values and you have a choice. You can
repeat that for the rest of the cells (ok if you like that kind of thing and don't have anywhere else
that you should be for a while), or you could do the good old-fashioned copy and paste - it works
the same but slower OR you can do the 'Nifty Short Cut'.
Quality of Measurement Task                                                                    Page 16
What is the 'Nifty Short Cut' for copying a formula down a column?
You should by now have seen that your mouse looks like three things:

        The mouse pointer looks like this when used for selecting.

        The mouse pointer looks like this when used for copying/filling.

         The mouse pointer looks like this when used for moving.




Move the pointer so that it rests on the little black box in the bottom right hand corner of cell C2
and looks like the copying/filling pointer above. Then double click. Hey presto, the formula is
copied all the way down your table.

Except that you now have a horrendous number of decimal places in most of the cells. If you are
saying 'What is horrendous about that number of decimal places' imagine measuring the
circumference of the Earth to the nearest centimetre. Fairly unlikely, huh?
If you just click the 'decrease decimal place' button again nothing will happen because of the
#/DIV/0! You can get rid of the offending item by just clicking on the cell and pressing delete or
highlighting and deleting #/DIV/0! in the formula bar. Now highlight the numbers and reduce the
decimal places to a decent number [2 or 3 because that is what was given in the data - probably 2].


How do I use Excels built in formulae?

Right, now we want the to work out the resistance of our resistor. We'll need the average, but Excel
has that function, along with many others, built in.

Click on cell B9 and type 'Average'.
Click on C9 and hit the = again to the left of the formula bar.
Click the button to the right of 'SUM' and select 'AVERAGE'.

Excel looks for the likeliest set of numbers you might be wanting to average and says is that it. If
you look at what it has done, it has selected C3:C8.

Click OK. The resistance should be 4.0Well done! That's the tricky bit over.

Formula symbols you will need in the future:
  plus                +                                     Things for you to try:
  minus               -
  multiply            *                                          Can you work out the power using P =
  divide              /                                           V x I for each of our readings?
   2
  a                   a*a or a^2
  10 3
                      10^3 or 1E3                                There is another formula for power P
  10-9                10^-9 or 1E-9                               = I2R. Make another column and
  3                  SQRT(3)                                     check that you get the same results as
                    PI                                          above.
  Sin()             SIN(80)


Quality of Measurement Task                                                                     Page 17
How do I do graphs?
Select the cells you wish to use for your graph - here it would be A2 to B8 - highlight them.
Select 'Chart Wizard' (if the button isn't there go to Insert then Chart.)

999,999 times out of 1,000,000 we will want an x-y scatter graph because it's scientific. I know 3D
doughnut shaped graphs look much sexier but don't be distracted.

Step 1. Select X-Y (scatter). Select the points without the line (top box). Click Next.

Step 2. Click Next.

Step 3. In Chart Title highlight 'Current (A)' and delete it. Type ' Current /Voltage graph for a
Resistor' then Enter. In Value (X) axis type 'Voltage (V)' then Enter, in Value (Y) axis type
'Current (A)' then Enter. Click on the Legend tab at the top of this box and click on the box with
the tick in it (show legend). It should now not have a tick in it. Click Next.

Step 4. Select top dot - as new sheet. Highlight Chart 1 and delete it. Type 'IV graph'. Click Finish.

You can play with your chart and make it pretty. If you right click anywhere on your chart and
select Format Plot area then you can change the background area (none is good!)




Now we can add a line and see what the equation is.
Click on any point and all the points should be highlighted. Click Chart on the menu line, then
Add Trendline. 'Linear' should be selected already. Click the Options tab at the top of the box.
Select 'Set Intercept = 0' and 'Display equation on chart'. Click OK.

Quality of Measurement Task                                                                     Page 18
The equation should be y = 0.2511x.

      Oh look. If the resistance is 4  then the conductance is ¼ S = 0.25S.
      And the conductance is also the gradient of an I vs. V graph. Well done Excel.



How do I change it so it plots V against I or P against I?

1. V against I instead of I against V.
Select the cells you wish to use for your graph - here it is A2 to B8 again- highlight them.
Select 'Chart Wizard'

Step 1. Select X-Y (scatter). Select the points without the line (top box). Click Next.

Step 2. Click on the Series tab at the top of the box then click on the funny looking button the right
of 'X values=Sheet1!$A$2:$A$8'. This takes you to this screen:




                                                                              Funny looking
                                                                              button




                         Highlight this
                         column




Highlight the numbers in the Current column not including the title or the word 'Average'. Click the
funny looking button again. Click on the funny looking button the right of 'Y =Sheet1!$B$2:$B$8'.
This time highlight the numbers in the Voltage column but not the title then click that button again.
Click Next.

Step 3. Add titles as before and remove legend. Click Next.

Step 4. Select top dot - as new sheet. Highlight Chart 1 and delete it. Type 'VI graph'. Click Finish.


Quality of Measurement Task                                                                    Page 19
If you now add a trendline, make sure that it goes through 0, you should find that the gradient is 4,
as you would expect.

2. P against I instead of I against V.
Select the cells you wish to use for your graph - here it is B1 to D8 because that selection includes
just current and power. Highlight them.
Select 'Chart Wizard'

Step 1. Select X-Y (scatter). Select the points without the line (top box). Click Next.

Step 2. Click on the Series tab at the top of the box then in the 'Series' box make sure that
'Resistance' is highlighted then click on the Remove as below. Click Next.




                                                              Click here




Step 3. Add titles as before and remove legend. Click Next.

Step 4. Select top dot - as new sheet. Highlight Chart 1 and delete it. Type 'PI graph'. Click Finish.


Hmm. Is there a less fiddly way?

If you like you can highlight the column that contains the numbers that you want on the bottom (x-
values) and copy and paste them to a place below your original table. Then copy what you want to
be up the side and paste it next to it. The only problem you will have will be if your columns
contain formulae. Then it will come up with #REF! To fix it try again but don't paste. From the
Edit menu select Paste Special, then Values. Then just do chart wizard and you won't have to
mess around with the series bit at all.

Quality of Measurement Task                                                                     Page 20
Let's get fancy…

1.  and other fancy symbol. These, just like in Word, are Greek letters. Click on your
   Resistance box, the click in the formula bar. Type (W) - make sure that it is capital W - then
   highlight the W. Go to Format, Cells, Font and select Symbol. A weird thing will happen. It
   will still say W in the formula line, but it will say in the column heading.
2. Renaming sheets. Point to where it says 'Sheet 1' then right click and select Rename (or go to
   Format, Sheet, Rename). Call it what you like.
3. Changing the lines on my chart. Instead of the statutory horizontal lines on your chart you can
   change it.
      Point at anywhere outside of the chart and right click and select Chart Options. On the
      Gridlines tab select Value X axis Major gridlines.
      Point at any of the grid lines and right click and select Format Gridlines. On the Scale tab
      try changing the values.
      Point at the x axis line and right click and select Format Axis. On the Patterns tab select
      Minor Tick Mark type Outside. See what happens.




Quality of Measurement Task                                                              Page 21

				
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