Question

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:

• A. Both P and Q are equally accurate but P is more precise than Q.
• B. P is more accurate but less precise than Q.
• C. P is less accurate but more precise than Q.
• D. Both P and Q are equally precise but P is more accurate than Q.

Hint:

Remember: Accuracy is about hitting the bullseye on average. Precision is about having a tight cluster of arrows, regardless of where they land.

Answer 1

The Correct Option is A

Step 1: Separate the two ideas clearly.
Accuracy means how close your average reading sits to the true value of 9.0. Precision means how tightly your readings cluster together, no matter where the true value is. Two students can be tight but off, or scattered but centred, so we must judge both separately.

Step 2: Find each student's average.
Take the three readings of student P and average them, then do the same for student Q. The student whose average lands nearer to 9.0 is the more accurate one. This single comparison settles the accuracy part.

Step 3: Compare the spreads.
Now look at how far apart the three readings are within each student's set. The student whose readings sit in a narrow band (small range or small spread) is the more precise one, even if that band is centred away from 9.0.

Step 4: Read the data pattern.
In this question, P's readings are bunched very tightly together but their centre is shifted away from the true 9.0. So P is highly precise but his centre is off, making him less accurate.

Step 5: Read Q's pattern.
Q's readings are more scattered, so Q is less precise, but their average happens to sit closer to the true 9.0, making Q the more accurate of the two.

Step 6: Combine the two judgments.
Putting it together, P is tight but off centre while Q is loose but better centred. So the correct reading of the data is that P is less accurate but more precise than Q.

\[ \boxed{\text{P is less accurate but more precise than Q}} \]