You can have two data sets with the same mean but different standard deviations.

Yes, it is possible to have two data sets with the same mean but different standard deviations. Here's how:

Step 1: Understanding Mean and Standard Deviation The mean is the average of a set of numbers, while the standard deviation measures the amount of variation or dispersion in a set of values.

Step 2: Creating Two Data Sets with the Same Mean For example, consider two data sets: Data set 1: 2, 4, 6 Data set 2: 4, 4, 4 Both data sets have the same mean of 4.

Step 3: Calculating the Standard Deviation However, the standard deviation of the first data set is 1.63 (rounded), indicating a greater dispersion of values around the mean. The standard deviation of the second data set is 0, as all values are the same and there is no dispersion.

So, it is indeed possible to have two data sets with the same mean but different standard deviations.