Two students (P and Q) independently made three measurements (denoted by I, II, and III) of the same property. The expected correct value is 9.0. The observed values by the students are provided in the given table.
Based on the given data, the correct statement is:
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Remember: Accuracy is about hitting the bullseye on average. Precision is about having a tight cluster of arrows, regardless of where they land.
Both P and Q are equally accurate but P is more precise than Q.
P is more accurate but less precise than Q.
P is less accurate but more precise than Q.
Both P and Q are equally precise but P is more accurate than Q.
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The Correct Option isA
Solution and Explanation
Step 1: Understanding the Question:
The question asks us to compare the accuracy and precision of the experimental measurements made by two different students, P and Q, against a true value of 9.0.
Step 2: Key Formula or Approach:
1. Accuracy refers to how close the average of the measurements is to the true/expected value:
\[ \text{Accuracy} \propto \frac{1}{|\text{Average} - \text{True Value}|} \]
2. Precision refers to how close the individual measurements are to one another, which is reflected by the range, standard deviation, or spread:
\[ \text{Spread} = \text{Maximum Value} - \text{Minimum Value} \]
Step 3: Detailed Explanation:
• Let us first evaluate the accuracy of both students' datasets.
• The true expected value is $9.0$.
• The average value calculated for Student P's measurements is:
\[ \text{Average}_P = \frac{8.9 + 9.1 + 9.0}{3} = 9.0 \]
• The average value calculated for Student Q's measurements is:
\[ \text{Average}_Q = \frac{8.0 + 9.0 + 10.0}{3} = 9.0 \]
• Since the average values for both students are exactly equal to the true value ($9.0$), both students are equally accurate.
• Next, let us evaluate the precision of both students' datasets by looking at the spread of their measurements.
• For Student P, the individual values are $8.9$, $9.1$, and $9.0$. The range is:
\[ \text{Range}_P = 9.1 - 8.9 = 0.2 \]
• For Student Q, the individual values are $8.0$, $9.0$, and $10.0$. The range is:
\[ \text{Range}_Q = 10.0 - 8.0 = 2.0 \]
• Since the spread/range of Student P's measurements ($0.2$) is much smaller than that of Student Q's ($2.0$), the individual measurements of P are much closer to one another.
• This indicates that Student P has a much higher level of precision.
Step 4: Final Answer:
Therefore, both P and Q are equally accurate, but P is more precise than Q.
