Question

1. two lab groups measure the length of an unknown object four different times. use their data below to answer the following questions.

group a: trial 1: 16.8 cm trial 2: 17.5 cm trial 3: 17.0 cm trial 4: 17.4 cm
group b: trial 1: 15.5 cm trial 2: 15.0 cm trial 3: 13.0 cm trial 4: 19.5 cm
a. what is the average length of group as data? (1 pt)
b. what is the average length of group bs data? (1 pt)
c. which groups data is more precise? why? (1 pt)
d. if the actual length of the object is 16.1 cm, which set of data is more accurate? why? (2 pts)
e. convert the actual length to kilometers. (1 pt)
f. which type of graph would be best for representing this type of data? justify your answer with reasoning.

Explanation:

Step1: Calculate Group A's average

Sum the lengths in Group A: $16.8 + 17.5+17.0 + 17.4=68.7$ cm. Then divide by 4. $\frac{68.7}{4}=17.175$ cm.

Step2: Calculate Group B's average

Sum the lengths in Group B: $15.5+15.0 + 13.0+19.5 = 63$ cm. Then divide by 4. $\frac{63}{4}=15.75$ cm.

Step3: Analyze precision

Precision refers to how close the measurements are to each other. Group B's values ($15.5, 15.0, 13.0, 19.5$) have a larger spread compared to Group A's values ($16.8, 17.5, 17.0, 17.4$). So Group A is more precise.

Step4: Analyze accuracy

Accuracy refers to how close the measurements are to the actual value. The actual length is 16.1 cm. The average of Group A ($17.175$ cm) has a difference of $|17.175 - 16.1|=1.075$ cm. The average of Group B ($15.75$ cm) has a difference of $|15.75 - 16.1| = 0.35$ cm. So Group B is more accurate.

Step5: Choose graph type

A bar - graph would be best for representing this data as it can clearly show the average values of each group side - by - side for easy comparison.

Step6: Convert to kilometers

We know that 1 km = 100000 cm. So, $16.1$ cm=$\frac{16.1}{100000}=0.000161$ km.

Answer:

a. Group A's average length: 17.175 cm
b. Group B's average length: 15.75 cm
c. Group A's data is more precise because its values are closer to each other.
d. Group B's data is more accurate because its average is closer to the actual length of 16.1 cm.
e. 0.000161 km
f. A bar - graph would be best for representing this data.