Question

Four different thermometers were used to measure the temperature of a sample of pure boiling water. The measurements are recorded in the table below.
Thermometer Temperature
Reading 1 Temperature
Reading 2 Temperature
Reading 3
W 100.1°C 99.9°C 96.9°C
X 100.4°C 102.3°C 101.4°C
Y 90.0°C 95.2°C 98.6°C
Z 90.8°C 90.6°C 90.7°C

The actual boiling point of pure water is 100.0°C.

What can be concluded from the data about the reliability and validity of the thermometers?​

Answer 1

Answer:

• Thermoter Z is the most reliable but has the least validity.

• Thermometer W has the highest validity.

• The rank for reliability, from most reliable to least reliable, is:              Z > X > W > Y

• The rank for validity, from greatest validy to lowest validity is:              W > X > Y > Z

Explanation:

Reliability is other name for the precision of the measurement, and it means how well the value is repeated; this is, how close the different measurements are one to each other. If the measurements are close one to each other, then the instrument is precise or reliable (high reliability).

Validity is other name for the accuracy of the measurement; this is, how close the measurement is to the true or accepted value.

With that we can compare the reliability (precision) and validity (accuracy) of the four different thermometers.

Repeat the table:

Temperatures in °C:

Thermometer  Reading 1   Reading 2   Reading 3

        W                 100.1             99.9             96.9

         X                 100.4           102.3             101.4

         Y                  90.0            95.2             98.6

         Z                  90.8             90.6            90.7

Reliability:

To analyze reliability (precision) we must compare the measures of every thermometer among them. A good approximation can be made calculating the range, i.e. the difference between the largest and the smallest readings:

• For W: largest reading - smallest reading = 100.1°C - 96.9°C = 3.2°C

• For X: largest reading - smallest reading = 102.3°C - 100.4°C = 1.9°C

• For Y: largest reading - smallest reading = 98.6°C - 90.0°C = 8.6°C

• For Z: largest reading - smallest reading = 90.8°C - 90.6°C = 0.2°C

Now, you conclude that the most reliable is thermometer Z and the least reliable is thermometer Y. The complete ranking, from most reliable to least reliable is:

• Z > X > W > Y

Validity:

To determine validity you must compare the mean of the three measures for each thermometer with the accepted value for the boiling point of pure water (100.0°C).

The mean is the sum of the trhee readings divided by 3.

The absolute error is calculated with the formula:

• absolute error = | accepted value - calculated value |.

The calculated value is the mean.

• For W: mean = (100.1 + 99.9 + 96.9)°C / 3 = 99.0°C

                    absolute error = 100.0°C - 99.0°C = 1.0°C

• For X: mean = (100.4 + 102.3 + 101.4)°C / 3 = 101.4 °C

                   absolute error = 101.4°C - 100.0°C = 1.4°C

• For Y: mean = (90.0 + 95.2 + 98.6)°C / 3 = 94.6°C

                   absolute error = 100.0°C - 94.6°C = 5.4°C

• For Z: mean = (90.8 + 90.6 + 90.7)°C / 3 = 90.7°C

                   absolute error = 100.0°C - 90.7°C = 9.3°C

Now you can rank the thermometers as per their validity (accuracy):

• 1.0°C < 1.4°C < 5.4°C < 9.3°C

• W is the most accurate, X is the second most accurate, Y is the third, and Z is the least accurate.