Question

Based on the two data sets given below, which of the following statements are true? Select two that apply.


Data Set 1: 5, 5, 6, 6, 7, 7
Data Set 2: 1, 3, 5, 7, 9, 11
(1 point)

Data Set 2 has the same mean as Data Set 1.

Data Set 2 has a smaller standard deviation than Data Set 1.

Data Set 2 has a larger standard deviation than Data Set 1.

Data Set 2 has a larger mean than Data Set 1.

Answer 1

True: Data Set 2 has the same mean as Data Set 1, and Data Set 2 has a larger standard deviation than Data Set 1.

Explanation: Both sums = 36 so both means = 36/6 = 6. SDs (population): Data Set 1 deviations: -1,-1,0,0,1,1 → variance = 4/6 ≈ 0.667 → SD ≈ 0.816. Data Set 2 deviations: -5,-3,-1,1,3,5 → variance = 70/6 ≈ 11.667 → SD ≈ 3.416. Hence same mean and Data Set 2 has the larger SD.