Question

question 4 of 10 three groups of students were tasked with determining the density of copper by water displacement. the data they collected is shown in the following table. a handbook lists the density of copper as 8.96 g/ml.

	group 1	group 2	group 3
trial 2 density (g/ml)	8.96	9.01	8.92
trial 3 density (g/ml)	8.97	9.01	8.86
average density (g/ml)	8.95	9.01	8.86

which group was most accurate?
○ group 1
○ group 3
○ group 2
which group was most precise?
○ group 2
○ group 1
○ group 3

Explanation:

Part 1: Which group was most accurate?

Accuracy refers to how close a measured value is to the true value (here, true density of copper is \( 8.96 \, \text{g/mL} \)). We calculate the absolute difference between each group's average density and the true density.

Step 1: Calculate error for Group 1

True density (\(
ho_{\text{true}} \)) = \( 8.96 \, \text{g/mL} \)
Average density of Group 1 (\(
ho_{\text{avg1}} \)) = \( 8.95 \, \text{g/mL} \)
Absolute error: \( |
ho_{\text{avg1}} -
ho_{\text{true}}| = |8.95 - 8.96| = 0.01 \, \text{g/mL} \)

Step 2: Calculate error for Group 2

Average density of Group 2 (\(
ho_{\text{avg2}} \)) = \( 9.01 \, \text{g/mL} \)
Absolute error: \( |9.01 - 8.96| = 0.05 \, \text{g/mL} \)

Step 3: Calculate error for Group 3

Average density of Group 3 (\(
ho_{\text{avg3}} \)) = \( 8.86 \, \text{g/mL} \)
Absolute error: \( |8.86 - 8.96| = 0.10 \, \text{g/mL} \)

Group 1 has the smallest absolute error (0.01), so it is the most accurate.

Part 2: Which group was most precise?

Precision refers to how close repeated measurements are to each other (low variability). We calculate the range (max - min) of each group’s trial densities (or use standard deviation, but range is simpler here).

Step 1: Calculate range for Group 1

Trial densities: \( 8.93, 8.96, 8.97 \)
Range: \( 8.97 - 8.93 = 0.04 \, \text{g/mL} \)

Step 2: Calculate range for Group 2

Trial densities: \( 9.02, 9.01, 9.01 \)
Range: \( 9.02 - 9.01 = 0.01 \, \text{g/mL} \)

Step 3: Calculate range for Group 3

Trial densities: \( 8.80, 8.92, 8.86 \)
Range: \( 8.92 - 8.80 = 0.12 \, \text{g/mL} \)

Group 2 has the smallest range (0.01), so it is the most precise.

Answer:

s:

• Most accurate: Group 1
• Most precise: Group 2

(For the multiple-choice format:
Which group was most accurate? \(\boldsymbol{\text{Group 1}}\)
Which group was most precise? \(\boldsymbol{\text{Group 2}}\))