Question

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. 22. what is the average length of group as data? a. 17.0 cm b. 16 cm c. 17.2 cm d. 68.7 cm. 23. which groups data is more precise? a. group a b. group b c. both d. neither. 24. if the actual length of the object is 16.1 cm, which set of data is more accurate? a. group a b. group b c. both d. neither

Explanation:

Step1: Recall average formula

The formula for the average (mean) of a set of data points \(x_1,x_2,\cdots,x_n\) is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\). For Group A, \(n = 4\), and the data - points are \(x_1=16.8\), \(x_2 = 17.5\), \(x_3=17.0\), \(x_4=17.4\).

Step2: Calculate sum for Group A

\(\sum_{i=1}^{4}x_i=16.8 + 17.5+17.0+17.4=68.7\).

Step3: Calculate average for Group A

\(\bar{x}_A=\frac{68.7}{4}=17.175\approx17.2\) cm.

Precision refers to how close the measured values are to each other. The values in Group B: 15.5, 15.0, 13.0, 19.5 have a larger spread compared to Group A: 16.8, 17.5, 17.0, 17.4. The values in Group A are closer to each other.

Accuracy refers to how close the measured values are to the true value. The true value is 16.1 cm. The average of Group A is approximately 17.2 cm and the values in Group A are all greater than 16.1 cm. The values in Group B are more spread out and also not close to 16.1 cm. None of the groups have values that are very close to 16.1 cm.

Answer:

1. C. 17.2 cm