Measurement Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Five measurements of the same object yield: {10.2,10.3,10.1,10.4,10.2}\{10.2, 10.3, 10.1, 10.4, 10.2\} grams. Calculate the mean and comment on the precision of the measurement process.

Solution

  1. 1
    Mean: xห‰=10.2+10.3+10.1+10.4+10.25=51.25=10.24\bar{x} = \frac{10.2+10.3+10.1+10.4+10.2}{5} = \frac{51.2}{5} = 10.24 g
  2. 2
    Range of readings: 10.4โˆ’10.1=0.310.4 - 10.1 = 0.3 g โ€” this is the random error spread
  3. 3
    Precision: readings cluster within 0.3 g, suggesting moderate precision; the mean 10.24 g is the best estimate of true weight

Answer

Mean = 10.24 g; random error range โ‰ˆ 0.3 g.
Repeated measurements reduce the effect of random error. The mean of multiple readings is a better estimate than any single reading. Spread of readings quantifies the random error inherent in the measurement process.

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 โ†’

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 medium

A scale consistently reads 0.5 kg too high (systematic error). A second scale gives variable reading

Example 4 hard

A thermometer reads the boiling point of water as 99.2ยฐC at sea level (true value: 100ยฐC). If 10 rep

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