Question

given the 3 sets of data below, rank the standard deviation in order from lowest to highest. set 1 = { -4, -2, 0, 2, 4} set 2 = {-15, -12, 0, 10, 15} set 3 = { 30, 30, 30, 30, 30} options: set 3, set 1, set 2; set 1, set 2, set 3; set 2, set 3, set 1; set 3, set 2, set1

Explanation:

Step1: Analyze Set 3

Set 3 has all values equal (30, 30, 30, 30, 30). The standard deviation (SD) of a set with all identical values is 0, as there's no variation. So \( \text{SD}_{\text{Set 3}} = 0 \).

Step2: Analyze Set 1

Set 1: \(\{-4, -2, 0, 2, 4\}\). These values are symmetric around 0, with small magnitudes. The spread (variation) is relatively low.

Step3: Analyze Set 2

Set 2: \(\{-15, -12, 0, 10, 15\}\). The values have larger magnitudes (e.g., -15, 15) and a wider spread compared to Set 1. So its SD is larger than Set 1's.

Step4: Rank SDs

From lowest to highest: Set 3 (SD=0) < Set 1 < Set 2.

Answer:

A. Set 3, Set 1, Set 2