Four different thermometers were used to measure the temperature of a sample of impure boiling water. The measurements are recorded in the table below.
| Thermometer | Temperature Reading 1 | Temperature Reading 2 | Temperature Reading 3 |
|---|---|---|---|
| W | $100.1^{\circ} C$ | $99.9^{\circ} C$ | $96.9^{\circ} C$ |
| X | $100.4^{\circ} C$ | $102.3^{\circ} C$ | $101.4^{\circ} C$ |
| Y | $90.0^{\circ} C$ | $95.2^{\circ} C$ | $98.6^{\circ} C$ |
| Z | $90.8^{\circ} C$ | $90.6^{\circ} C$ | $90.7^{\circ} C$ |
The actual boiling point of pure water is $100.0^{\circ} C$.
What can be concluded from the data about the reliability and validity of the thermometers?
A. Thermometer Y has the highest validity.
B. Thermometer Z is the most reliable.
C. Thermometer W is the most reliable.
D. Thermometer X has the highest validity.
Answer (1)
Calculate the average reading for each thermometer.
Calculate the standard deviation of the readings for each thermometer. Thermometer Z has the lowest standard deviation.
Calculate the absolute difference between the average reading of each thermometer and the actual boiling point. Thermometer W has the lowest absolute difference.
Conclude that Thermometer Z is the most reliable.
B
Explanation
Analyze the problem and data We have four thermometers (W, X, Y, and Z) used to measure the temperature of impure boiling water. We have three readings for each thermometer. The actual boiling point of pure water is 100. 0 ∘ C . We need to determine which conclusion about the reliability and validity of the thermometers can be drawn from the data.
Calculate average readings First, we calculate the average reading for each thermometer:
Thermometer W: W a vg = 3 100.1 + 99.9 + 96.9 = 3 296.9 = 98.9666... ≈ 98.9 7 ∘ C
Thermometer X: X a vg = 3 100.4 + 102.3 + 101.4 = 3 304.1 = 101.3666... ≈ 101.3 7 ∘ C
Thermometer Y: Y a vg = 3 90.0 + 95.2 + 98.6 = 3 283.8 = 94. 6 ∘ C
Thermometer Z: Z a vg = 3 90.8 + 90.6 + 90.7 = 3 272.1 = 90. 7 ∘ C
Calculate standard deviations Next, we calculate the standard deviation for each thermometer to assess reliability:
Thermometer W: The standard deviation is approximately 1.79 .
Thermometer X: The standard deviation is approximately 0.95 .
Thermometer Y: The standard deviation is approximately 4.33 .
Thermometer Z: The standard deviation is approximately 0.10 .
Lower standard deviation indicates higher reliability. Thus, thermometer Z is the most reliable.
Calculate validity Now, we calculate the absolute difference between each thermometer's average reading and the actual boiling point ( 100. 0 ∘ C ) to assess validity:
Thermometer W: ∣98.97 − 100.0∣ = 1.03
Thermometer X: ∣101.37 − 100.0∣ = 1.37
Thermometer Y: ∣94.6 − 100.0∣ = 5.4
Thermometer Z: ∣90.7 − 100.0∣ = 9.3
Lower absolute difference indicates higher validity. Thus, thermometer W has the highest validity.
Conclusion Based on our calculations, Thermometer Z is the most reliable because it has the lowest standard deviation ( 0.10 ). Thermometer W has the highest validity because its average reading is closest to the actual boiling point of pure water. Therefore, the correct answer is B.
Final Answer The correct answer is B. Thermometer Z is the most reliable.
Examples
Understanding thermometer reliability and validity is crucial in scientific experiments. For example, in a chemistry lab, accurate temperature measurements are essential for conducting experiments and recording data. Using a reliable and valid thermometer ensures that the experimental results are accurate and reproducible, which is vital for the advancement of scientific knowledge. Similarly, in medical settings, accurate temperature readings are necessary for diagnosing and treating patients effectively.
