Standard deviation is a measure of spread. The bigger the traditional deviation, the more spread the end the data is. Thus, the data collection with a typical deviation the 3 is less spread out than the data collection with standard deviation that 12. But they would both have actually the very same center.
You are watching: Explain how two samples can have the same mean
Though the 2 data sets have the exact same mean, the 2nd data set has a greater standard deviation. This method that scores in that data set will be an ext spread out roughly the typical value of 50 contrasted to the first data set.
If girlfriend think of a normal distribution, that will aid make the allude clear. In a typical distribution, roughly 68% of scores will fall within one typical deviation below and above the mean. So because that the an initial data set, approximately 68% the scores would fall between 47 and also 53. Because that the 2nd data set, top top the other hand, around 68% that scores would certainly fall in between 38 and 62. As you deserve to see, the scores in the data set with the greater standard deviation will certainly exhibit much more variability about the mean contrasted to the data set with the smaller standard deviation.
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