Question

which of the below data sets has the lowest standard deviation? you do not need to calculate the exact standard deviations to answer this question.
0, 1, 3, 3, 3, 5, 6
0, 25, 50, 100, 125, 150, 1000
0, 0, 0, 100, 200, 200, 200
0, 1, 2, 3, 4, 5, 6

Explanation:

Step1: Understand standard deviation concept

Standard deviation measures data spread. Less spread means lower standard deviation.

Step2: Analyze each data - set

• For \(0,1,3,3,3,5,6\): Values are somewhat spread.
• For \(0,25,50,100,125,150,1000\): There is a large out - lier (\(1000\)), so high spread.
• For \(0,0,0,100,200,200,200\): There is a gap between \(0\) and \(100\), so more spread.
• For \(0,1,2,3,4,5,6\): Values are evenly spaced with no extreme outliers or large gaps.

Answer:

\(0,1,2,3,4,5,6\)