What Makes the Standard Deviation Larger or Smaller? You will find 15 pairs of g

Question

What Makes the Standard Deviation Larger or Smaller? You will find 15 pairs of graphs on the next four pages. The mean for each graph (X) is given just above each histogram. For each pair of graphs presented below 1. Indicate whether one of the graphs has a larger standard deviation than the other or if the two graphs have the same standard deviation. 2. Try to identify the characteristics of the graphs that make the standard deviation larger or smaller. You can check your answers against the instructor's answer key as you complete each page. A has a larger standard deviation than B B has a larger standard deviation than A Both graphs have the same standard deviation A has a larger standard deviation than B B has a larger standard deviation than A Both graphs have the same standard deviation A has a larger standard deviation than B

Explanation / Answer

Answer to both the questions below:

1. B has more standard deviation than A, because the last score of A is lower, meaning lower weightage / lower frequency at higher score. If there is a lower weightage at extreme scores then the distribution will tend more to the center, indicating lower standard deviation.

2. The same distribution if more towards center would mean lesser deviation. Hence, B has a larger standard deviation than A

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