Measurement Math Example 4
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Example 4
hardA thermometer reads the boiling point of water as 99.2°C at sea level (true value: 100°C). If 10 repeated readings give mean 99.2°C with SD=0.3°C, identify the type(s) of error and suggest how to address each.
Solution
- 1 Systematic error: mean = 99.2°C vs. true 100°C; bias = 0.8°C — the thermometer consistently reads too low
- 2 Random error: SD = 0.3°C — each reading varies around 99.2°C due to random fluctuations
- 3 Address systematic: recalibrate the thermometer using a known reference (boiling point = 100°C at sea level)
- 4 Address random: take more readings and average them; the standard error of the mean is °C
Answer
0.8°C systematic bias + 0.3°C random error. Fix bias by calibration; reduce random error by averaging more readings.
Real measurements often have both types of error simultaneously. Systematic errors require process correction; random errors require more data. Standard error = SD/√n shows how the mean improves with more measurements.
About Measurement
Measurement is the process of assigning numerical values to attributes of objects or events according to a defined rule or scale.
Learn more about Measurement →More Measurement Examples
Example 1 easy
A ruler measures a pencil as 14.7 cm. The ruler has markings to the nearest 0.1 cm. Explain measurem
Example 2 mediumA scale consistently reads 0.5 kg too high (systematic error). A second scale gives variable reading
Example 3 easyFive measurements of the same object yield: [formula] grams. Calculate the mean and comment on the p