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 points from the mean indicates a larger standard deviation.

Step2: Analyze Set 1

Set 1: {10, 19, 38, 50, 51}. The values are somewhat spread out.

Step3: Analyze Set 2

Set 2: {5, 21, 26, 39, 51}. There is a spread, but not as extreme as some others.

Step4: Analyze Set 3

Set 3: {9, 38, 50, 50, 51}. The repeated value of 50 reduces the spread compared to some sets.

Step5: Analyze Set 4

Set 4: {5, 28, 28, 28, 51}. There are repeated 28s, but the difference between 5 and 51 creates a relatively large spread. Comparing the sets, Set 1 has the largest spread of values from the mean.

Answer:

Set 1