Same mean, different standard deviation in data sets?

Question

How would a data set containing the values of a variable with a mean of 50 and a standard deviation of 3 compare with another data set containing the same variable, but a mean of 50 and a standard deviation of 12?

Answer 1

Standard deviation is a measure of spread. The larger the standard deviation, the more spread out the data is. Thus, the data set with a standard deviation of 3 is less spread out than the data set with standard deviation of 12. But they would both have the same center.

Answer 2

Hi Moriah,

Though the two data sets have the same mean, the second data set has a higher standard deviation. This means that scores in that data set will be more spread out around the mean value of 50 compared to the first data set.

If you think of a normal distribution, it will help make the point clear. In a normal distribution, approximately 68% of scores will fall within one standard deviation below and above the mean. So for the first data set, approximately 68% of scores would fall between 47 and 53. For the second data set, on the other hand, approximately 68% of scores would fall between 38 and 62. As you can see, the scores in the data set with the higher standard deviation will exhibit much more variability around the mean compared to the data set with the smaller standard deviation.

Hope this answer helps!

-Mike