A large standard deviation indicates that the distribution is heavily weighted far from the mean. Take the following example:
{1,1,1,1,1,19,19,19,19,19} Mean is 10 and StDev = 9.49
Now look at this data set: {5, 6, 7, 8, 9, 11, 12, 13, 14, 15}
Mean is still 10, but StDev = 3.5
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True.
If all four numbers are the same, there is no standard deviation. The mean will be equal to all 4 numbers, resulting in a 0 standard deviation. Ex) 5,5,5,5
One standard deviation
Mean 0, standard deviation 1.
Mean = 0 Standard Deviation = 1