High School

Measurement errors are a type of uncertainty involved in single measurements. Suppose we measure the diameter of a disk, where the minimum length that can be measured on the stick is 1 mm (0.1 cm). If the diameter lies somewhere between 5.1 cm and 5.2 cm, which value do we report? In such cases, the value is reported as 5.15 ± 0.05 cm. Note that the uncertainty of the measurement is half the smallest tick mark on the measuring device, and this applies to all instruments.

A sound experimental procedure involves several measurements of the required physical quantities. Once those measurements have been made, we compute the statistical quantities listed in the key concepts to make inferences from the data obtained.

**Question 1:**

(Write down answers on Report Sheets)

Below are three sets of measurements of the boiling point of water at 1 standard atmosphere (atm):

| Measurement | 1 | 2 | 3 | 4 | 5 |
|-------------|---|---|---|---|---|
| Set A | 99.8 °C | 99.8 °C | 99.8 °C | 99.8 °C | 99.8 °C |
| Set B | 100.0 °C | ... | ... | ... | ... |

(Note: The completion of Set B's data was not provided in the initial text.)

Answer :

Answer:

T = (99.78 ±0.05) ºC

Explanation:

This problem refers to the procedure to perform the measurements and their correct reporting.

Suppose that the thermometer used has an appreciation of 0.1ºC and the values ​​of 5 measurements resulted in

# T (ºC)

1 99.8

2 99.7

3 99.7

4 99.8

5 99.9


the processing calculate mean value

T_average = ∑ [tex]T_{i}[/tex] / n

T_average = (99.8 + 99.7 + 99.7 + 99.8 + 99.9) / 5

T_average = 99.78ºC


the absolute error or uncertainty of the measurement is half the appreciation of the instrument

ΔT = ± 0.05ºC


so the result must be written

T = (99.78 ±0.05) ºC

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