Estimating Standard Deviation Both data sets ...

Question

Estimating Standard Deviation Both data sets shown in the stem-and-leaf plots have a mean of 165. One has a standard deviation of 16, and the other has a standard deviation of 24. By looking at the stem-and-leaf plots, which is which? Explain your reasoning.

Stem-and-leaf plot displaying two data sets with a key for interpretation.

Accepted Answer

Welcome back, everyone. The two stem and leaf plots below represent test scores from two different classes. Both classes have an identical mean score of 75. However, one class has a standard deviation of 5, while the other has a standard deviation of 12. Which plot corresponds to the class with the higher standard deviation? Explain your reasoning. Here are plots A and B. And for our answer choices, ASS plot A has the highest standard deviation because it has more data points above 80. B says plot B has the highest standard deviation because the data points are spread over a larger range of values, showing more variability. C says plot A has the higher standard deviation because its scores are closer to the mean. And D says plot B has the higher standard deviation because it contains more scores near the mean reducing variability. Now let's look at both of our plots. Let's start with plot A. Now, if we can know which, or we can get a sense of how spread out the data values are by looking at the STEM plate. Now, in plot A, notice here that our range. Uh, the values go from 68 to 82 because here we have the key 68 equals 68. So our range is gonna be 82 minus 68, which equals 14. So we have a narrow range of 14 points. Notice here that most scores are clustered closely around the mean. The mean is 75 and most of the scores are between 70 and 80. And thus this tight clustering means the data values don't deviate far from the mean, which means that this is likely a low standard deviation. OK? So in this case, we can say here that we have some tight clustering for plot A. Now how does it compare to plot B? Well, no, notice that in plot B here our range, OK, goes from 45. The values go from 45 to 101. So the range is 101 minus 45, which equals 56. So plot B has a much wider spread of 56 points. Notice here that the data is more spread out, with several scores far below the mean, OK, going from 45 all the way up to uh 67 here. And then we also have several scores above the mean, OK, uh, going here, we have it 96 uh up to 101. And so on, OK? In this case, we know the mean is 75, so we also have quite a few more values here ranging from 76 up to 101. So this wider spread means the data deviates more from the mean, resulting in a higher standard deviation. And if that's the case, that means it's more likely that plot B, OK. Corresponds To a standard deviation of 12, while plot A corresponds to a standard deviation of 5. OK. So, that means B is the correct answer. Plot B has the highest standard deviation because the data points are spread over a large range of values showing more variability. Thanks a lot for watching everyone. I hope this video helped.

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