Question

1. graphical reasoning both data sets represented below have a mean of 50. one has a standard deviation of 2.4, and the other has a standard deviation of 5. by looking at the graphs, which is which? explain your reasoning.

Explanation:

Step1: Recall standard deviation concept

Standard deviation measures the spread of data. A smaller standard deviation means data is more clustered around the mean; a larger one means data is more spread out.

Step2: Analyze the two graphs

• Graph (a): Data points are more clustered (taller, narrower peak) around the mean (50). So it has a smaller spread.
• Graph (b): Data points are more spread out (shorter, wider peak) around the mean (50). So it has a larger spread.

Step3: Match with standard deviations

Since 2.4 < 5, the more clustered graph (a) has a standard deviation of 2.4, and the more spread - out graph (b) has a standard deviation of 5.

Answer:

Graph (a) has a standard deviation of 2.4, and Graph (b) has a standard deviation of 5. This is because standard deviation measures data spread: a smaller standard deviation (2.4) corresponds to data more clustered around the mean (seen in graph (a)), and a larger standard deviation (5) corresponds to data more spread out (seen in graph (b)).