WORKING SCIENTIFICALLY: ERRORS, Fair Test etc.

- Outlier/Anomalies

These are values in a set of results which are judged not to be part of the variation caused by random uncertainty.

Question 1: Matthew records the current in a resistor for a certain voltage and takes repeat readings, some of which are shown below:

Resistance (Ω) |
current (A) |
||||

1 | 2 | 3 | 4 | mean | |

20 | 0.25 | 0.28 | 0.47 | 0.26 | |

30 | 0.16 | 0.17 | 0.15 | 0.16 |

- Highlight the anomaly/outlier in the table.
- Correctly determine the mean for each row.

- Measurement error: The difference between a measured value and the true value.

Question 2: Simon measures the mass of a mug as being 250 g, but its true value is actually 260 g. The difference is a measurement error.

(True value is the value that would be obtained in an ideal measurement. An ideal measurement is one that would have no errors at all)

Calculate the percentage error in Simon’s measurement.

- Uncertainty

The interval within which the true value can be expected to lie, with a given level of confidence or probability, e.g. “the temperature is 20°C ± 2°C, at a level of confidence of 95%.”

The symbol ± is called “plus or minus”, and in the example above means “plus or minus 2°C” – i.e. the temperature is most likely to be between 18°C and 22°C.

The “level of confidence” expresses **how certain** the scientists are of their claim that the temperature is in the range 18—22°C.

Question 3:(a) State the mean and the uncertainty for the following data:

33, 36, 28, 37, 29, 27, 30, 31

Question 4: In conducting an experiment comparing the speed of sound to the air temperature, Amasha’s thermometer has units of 1 o C and you have found the air temperature to be 20 o C. Calculate

- The absolute uncertainty
- The percentage uncertainty.

- Random Errors

These cause readings to be spread about the true value, due to results varying in an unpredictable way from one measurement to the next.

Random errors are present when any measurement is made, and cannot be corrected. The effect of random errors can be reduced by making more measurements and calculating a new mean.

Random errors may be caused by human error, a faulty technique in taking the measurements, or by faulty equipment.

Question 5: Fawad and Andrew are both timing a very fast pendulum with a stopwatch. Andrew can’t count the swings accurately as it is just too fast to keep up – this introduces a random error in his readings as he may think he has counted 20 swings when in fact it was 21.

Fawad doesn’t use the stopwatch very well. Although he starts it fairly accurately, he panics when having to stop it and is either too early or late. This is a random *human* error.

Suggest how Fawad and Andrew can improve the reliability of their data. Explain your answer.

Question 6: Matthew records the current in a resistor for a certain voltage and takes repeat readings, some of which are shown below:

Resistance (Ω) |
current (A) |
||||

1 | 2 | 3 | 4 | mean | |

20 | 0.25 | 0.28 | 0.47 | 0.26 | |

30 | 0.16 | 0.17 | 0.15 | 0.16 |

- Explain how Matthew’s table shows a random error.
- Explain how to improve the accuracy of the data in Matthew’s experiment.

- Systematic errors

These cause readings to differ from the true value by a consistent amount each time a measurement is made.

Sources of systematic error can include the environment, methods of observation or instruments used.

Systematic errors cannot be dealt with by simple repeats. If a systematic error is suspected, the data collection should be repeated using a different technique or a different set of equipment, and the results compared.

e.g. A systematic error occurs when using a wrongly calibrated instrument.

E.g. Ashley’s pendulum timing experiment was made worse by the fact that she also began counting at ‘1’ not ‘0’. So all her times, in addition to random in her counting, were also short of one full swing each making her calculated times all smaller than the ‘true values’.

7 FAIR TEST

A fair test is one in which only the independent variable has been allowed to affect the dependent variable.

A fair test can usually be achieved by keeping all other variable constant.

Question 7

Swee Yong and Pavan are investigating how the **electrical resistance** of wires changes with length. Unfortunately both of them let the current get too high for shorter wires, which dramatically increases their temperature. Since temperature affects resistance (in addition to the length), it is **not** a fair test.

- Identify the independent and dependent variables in their investigation.
- Explain why their experiment is not a fair test.
- What could they do to make it a fair test?