Question

four data sets are shown below: set 1: {10, 19, 38, 50, 51} set 2: {5, 21, 26, 39, 51} set 3: {9, 38, 50, 50, 51} set 4: {5, 28, 28, 28, 51} which data set has the largest standard deviation?

Explanation:

Step1: Recall standard - deviation concept

Standard deviation measures the amount of variation or dispersion of a set of values. A larger spread of data from the mean indicates a larger standard deviation.

Step2: Analyze Set 1

Set 1: $\{10,19,38,50,51\}$. The values are more spread out from each other. The differences between consecutive values vary significantly.

Step3: Analyze Set 2

Set 2: $\{5,21,26,39,51\}$. The data points are somewhat clustered compared to Set 1. For example, 21 and 26 are close together.

Step4: Analyze Set 3

Set 3: $\{9,38,50,50,51\}$. There are repeated values (50 twice), which reduces the overall spread compared to a set with all distinct values with similar range.

Step5: Analyze Set 4

Set 4: $\{5,28,28,28,51\}$. There are three repeated 28s, making the data less spread out. The repeated values pull the data towards the mean, reducing the standard - deviation.

Answer:

Set 1