How would a data set containing the values of a variable with a expect of 50 and also a traditional deviation of 3 compare through one more data collection containing the very same variable, yet a expect of 50 and also a traditional deviation of 12?

Standard deviation is a meacertain of spreview. The larger the traditional deviation, the more spcheck out out the information is. Hence, the data set through a conventional deviation of 3 is much less spcheck out out than the data collection through typical deviation of 12. But they would certainly both have the very same center.

You are watching: How can two samples have the same mean but different standard deviations

Hi Moriah,

Though the two information sets have actually the same suppose, the second data collection has a greater traditional deviation. This suggests that scores in that data set will certainly be more spread out around the mean worth of 50 compared to the first data collection.

If you think of a normal distribution, it will help make the suggest clear. In a normal distribution, about 68% of scores will certainly autumn within one conventional deviation listed below and also above the intend. So for the initially data collection, about 68% of scores would certainly loss between 47 and also 53. For the second data set, on the other hand, approximately 68% of scores would autumn in between 38 and also 62. As you deserve to see, the scores in the data set through the greater typical deviation will certainly exhilittle bit a lot even more variability approximately the expect compared to the data collection with the smaller sized standard deviation.

-Mike

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