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The length of track for train track is being measured for a new rail system in Phoenix. The sections are manufactured to each measure 100 feet. A sample of 20 track sections is taken at random, and measured using a standard metal tape. The temperature outside where the first 10 measurements are taken is about 85 oF, and the temperature when the 2nd 10 measurements are taken is about 110 oF. Here is the data: 85o 100.2 100.2 100.1 100.3 100.1 100.2 100.4 100.5 100.4 100.2 110o 100.1 100.3 99.8 99.6 100.2 99.5 100.4 99.9 99.9 100.5. Which of the two sets of measurements shows the least precision in measurement?

Answer :

To determine which set of measurements is the least precise, we need to look at how much variation or dispersion there is within each set of data.

First, recall that precision refers to the consistency of repeated measurements. The more similar the measurements are to each other, the greater the precision.

Let's examine both data sets:

Measurements at 85°F:

  • 100.2, 100.2, 100.1, 100.3, 100.1, 100.2, 100.4, 100.5, 100.4, 100.2

Measurements at 110°F:

  • 100.1, 100.3, 99.8, 99.6, 100.2, 99.5, 100.4, 99.9, 99.9, 100.5

One way to measure precision is to calculate the range, which is the difference between the maximum and minimum values in each set. A smaller range indicates greater precision.

  1. Range for 85°F Measurements:

    • Maximum: 100.5
    • Minimum: 100.1
    • Range = 100.5 - 100.1 = 0.4

  2. Range for 110°F Measurements:

    • Maximum: 100.5
    • Minimum: 99.5
    • Range = 100.5 - 99.5 = 1.0

The range at 85°F is 0.4, whereas the range at 110°F is 1.0. This indicates that the set of measurements taken at 110°F has more variability and is less precise compared to the set taken at 85°F.

Thus, the measurements taken at 110°F show the least precision in measurement.

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