To determine which distribution of data has the largest standard deviation, let's analyze the given distributions and their standard deviations:
1. Data set: \(1, 1, 1, 1, 4, 4, 7, 7, 7, 7\)
- Standard Deviation: \(2.6832815729997477\)
2. Data set: \(1, 1, 1, 4, 4, 4, 4, 7, 7, 7\)
- Standard Deviation: \(2.32379000772445\)
3. Data set: \(1, 1, 4, 4, 4, 4, 4, 4, 7, 7\)
- Standard Deviation: \(1.8973665961010275\)
4. Data set: \(1, 4, 4, 4, 4, 4, 4, 4, 4, 7\)
- Standard Deviation: \(1.3416407864998738\)
From these given standard deviations, we can determine that:
- The first data set has the largest standard deviation of \(2.6832815729997477\).
This means that the data set [tex]\(1, 1, 1, 1, 4, 4, 7, 7, 7, 7\)[/tex] has the largest standard deviation among the provided distributions. This indicates that the values in this distribution are more spread out from the mean compared to the other data sets.
