Question

question 2. three students were asked to determine the volume of a liquid by a method of their choosing. each performed three trials. the table below shows the results. the actual volume of the liquid is 24.8 ml.

a) considering the average of all three trials, which students measurements show the greatest accuracy?

b) which students measurements show the greatest precision?

Explanation:

Step1: Calculate average for Student A

Average = $\frac{24.8 + 24.8 + 24.4}{3} = \frac{74}{3} \approx 24.67$ mL
Difference from actual: $|24.67 - 24.8| = 0.13$ mL

Step2: Calculate average for Student B

Average = $\frac{24.2 + 24.3 + 24.3}{3} = \frac{72.8}{3} \approx 24.27$ mL
Difference from actual: $|24.27 - 24.8| = 0.53$ mL

Step3: Calculate average for Student C

Average = $\frac{24.6 + 24.8 + 25.0}{3} = \frac{74.4}{3} = 24.8$ mL
Difference from actual: $|24.8 - 24.8| = 0$ mL

Step4: Compare differences for accuracy

Student C's average equals actual volume (smallest difference).

Step5: Analyze precision (data spread)

Student A: $24.4, 24.8, 24.8$ → range = $24.8 - 24.4 = 0.4$ mL
Student B: $24.2, 24.3, 24.3$ → range = $24.3 - 24.2 = 0.1$ mL
Student C: $24.6, 24.8, 25.0$ → range = $25.0 - 24.6 = 0.4$ mL
Student B has smallest range (most consistent).

Answer:

a) Student C
b) Student B