Successfully reported this slideshow.
Upcoming SlideShare
×

# Uncertainty and equipment error

94,804 views

Published on

• Full Name
Comment goes here.

Are you sure you want to Yes No
• re slide 6, could you pls explain more about interval measurement uncertainty

Are you sure you want to  Yes  No
• Njce! Thanks for sharing.

Are you sure you want to  Yes  No

### Uncertainty and equipment error

1. 1. Uncertainty andEquipment Error by Chris Paine Bioknowledgy
2. 2. Absolute uncertainty and recording data   When you record measurements you should also record the (absolute) uncertainty associated with the measurement  The uncertainty reflects greatest precision, i.e. the smallest unit to which a measurement can be made. This method of quoting uncertainty is called least count
3. 3. Absolute uncertainty and recording data  For example measuring a length:   We measure a length of 213 mm   The smallest unit on a ruler is 1mm therefore the uncertainty is (±1 mm)   Therefore as we know the value should be no less than 212 mm and no more than 214 mm   Therefore we can quote the value as 213 mm (±1 mm)
4. 4. Uncertainties and recording data  It is illogical to report values with more decimal places than that indicated by the uncertainty for example:   9.63 ± 0.6 the last decimal place has no meaning and the number should be reported as 9.6 ±0.6  If a value 48cm3 is measured to an uncertainty of ±0.5cm3 it should be quoted as 48.0cm3 (±0.5 cm3) – this is an IBO guideline
5. 5. What about uncertainties in processed data?  If means and standard deviations are calculated from a data set. Therefore they should be quoted in the same units and the same uncertainty as the data they are calculated from.  For example: 10 mm (±1 mm) 12 mm (±1 mm) 14 mm (±1 mm)  Mean = (10 mm + 12 mm + 14 mm) / 3 = 12 mm (±1 mm)  Standard deviation = 2 mm (±1 mm)
6. 6. Deciding on the level of uncertainty  Uncertainty may be quoted on a piece of apparatus or in it’s manual – use that  If this information is not available use the least count method  You may choose to increase your uncertainty to reflect the way a piece of equipment is used. Justify this decision in your lab report.  Time is different, stopwatches depend both on the reaction time of the user and how they are used:   It takes us 0.1 – 0.3 seconds to start and stop a watch. Therefore the uncertainty is in the region of ±1s   If you are taking interval measurements, e.g. you observe an investigation every 2 minutes then your uncertainty is the same as your interval ±2 min
7. 7. Examples of uncertainty  For example, the school electronic balances measure to 1/100th of a gram e.g. 2.86 g The precision of the electronic balance is ±0.01 g Hence the reading on the electronic balance should be reported as 2.86 g (±0.01 g)  When using a ruler we can usually be accurate to the nearest mm The implied limits of the measurement 28 mm are 27 mm – 29 mm This can be written as 28 mm (±1 mm), where the ±1 mm is the absolute uncertainty  N.B. Quote the uncertainty in the column header (e.g. ±0.01 g or ±1 mm) of your data table rather than against each
8. 8. Be careful of Repeated equipment use  “I use a 300 mm ruler to measure 970 mm, what is the uncertainty?” “To measure the length I must of used the ruler 3 times (300 mm + 300 mm + 270 mm)” “Hence the uncertainty in my measurements is 3 times as big (1 mm + 1 mm + 1 mm)” “Therefore my measurement is 970 mm (±3 mm)” N.B. In reality the investigator should have made a better choice of equipment, e.g. 1m ruler
9. 9. Be careful of Repeated equipment use  “I am carrying out a vitamin C titration in a 50cm3 burette with an uncertainty of ±0.05cm3. My starting volume reads 48cm3. When I finish my titration the volume reads 35.6cm3.” “The volume I used in the titration is 12.4cm3 (48cm3 – 35.6cm3)” “I took two reading from the burette therefore my uncertainty doubled to ±0.1cm3 (±0.05cm3 + ±0.05cm3)” “Therefore my volume is 12.4cm3 (±0.1cm3)”
10. 10. Systematic Error  Analysis of systematic error looks at how rigorously your method controlled, varied and measured the different variables  One aspect is equipment error, i.e. was the equipment choice and use appropriate?  Ideally equipment errors ideally should be below 5%
11. 11. Equipment Error  Although it is optional to assess equipment errors it is highly recommended  For each different use of equipment calculate the % error  Calculate the error on the smallest quantity measured. The smallest quantity will generate the largest error.  Ideally equipment errors ideally should be below 5%  Repeated calculations can be useful to illustrate cases where only a couple of measurements break the 5% error rule. Use your judgment.
12. 12. Calculating % equipment errors  Use a table to organise the calculations  The table enhances the evaluation therefore add to the evaluation section of the lab report Measuring Uncertainty Smallest % Error Instrument amount and use measured (= uncertainty x 100 / amount measured)
13. 13. Example Calculations  13 mm was the smallest length measured  1 mm the uncertainty  % Equipment Error = uncertainty x 100 / amount measured  = 1 mm x 100 / 13  = 6.7 %
14. 14. Evaluation - What if an Equipment Error is greater than 5%?  Recommend a change to a more accurate named example of measuring equipment  Suggest than larger (suggest an amount) amounts are measured/sampled to bring error below 5%
15. 15. Evaluation – what if equipment errors are below 5%?  It’s not necessary to suggest a change, but still comment on it to show that you’ve critically evaluated your equipment use.
16. 16. Design - make sure you are measuring the right amounts  If % Equipment Error = uncertainty x 100 / amount measured  Then amount measured = uncertainty x 100 / % Equipment Error  Therefore smallest amount measured ≥ uncertainty x 20