Question

given the two distributions below, which has the smaller standard - deviation? how do you know? variable a has a smaller standard deviation because more of the observations have values closer to the mean than variable bs distribution. variable b has a smaller standard deviation because more of the observations have values closer to the mean than variable as distribution. the standard deviations appear to be approximately equal because both distributions are centered near 5. variable a has a smaller standard deviation because its peak is lower than variable bs distribution.

Explanation:

Step1: Recall standard - deviation concept

Standard deviation measures the spread of data. Data points closer to the mean result in a smaller standard deviation.

Step2: Analyze the histograms

In Variable B's distribution, more data points are clustered around the mean compared to Variable A. This means the values in Variable B deviate less from the mean.

Answer:

Variable B has a smaller standard deviation because more of the observations have values closer to the mean than in Variable A's distribution.