Table of Contents
- 1 What is the smallest possible value of the standard deviation?
- 2 How do you find the smallest standard deviation?
- 3 Is there more than one possibility for choosing four numbers that have the smallest possible standard deviation?
- 4 Which dataset has lowest standard deviation?
- 5 What is low standard deviation?
- 6 What does smaller standard deviation mean?
What is the smallest possible value of the standard deviation?
The smallest possible value for the standard deviation is 0, and that happens only in contrived situations where every single number in the data set is exactly the same (no deviation).
How do you find the smallest standard deviation?
Step 1
- The smallest possible standard deviation is 0, because the standard deviation is nonnegative.
- The standard deviation will be zero, if all data values are equal.
- A possible data list is then: 2, 2, 2, 2.
- But you could also pick, for example, 10, 10, 10, 10.
Which set of four numbers has the largest possible standard deviation?
Here are five different sets of four numbers. As you can see, the set {0, 0, 10, 10} does have the largest possible standard deviation.
Is there more than one possibility for choosing four numbers that have the smallest possible standard deviation?
Step 2: Is there more than one possibility for choosing four numbers that have the smallest possible standard deviation? No.
Which dataset has lowest standard deviation?
Whilst all the values in set B are relatively close to the mean, set A’s values are all within one of the mean. Five of the values are 41, one of the values is 42, and the mean is 41.16 recurring. This means that set A would have the lowest standard deviation as the variation from the mean is lowest.
Would it be possible to have a set of 5 numbers where the standard deviation is 0?
Yes, it is possible for the standard deviation of a list of numbers to equal 0.
What is low standard deviation?
Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out. A standard deviation close to zero indicates that data points are close to the mean, whereas a high or low standard deviation indicates data points are respectively above or below the mean.
What does smaller standard deviation mean?
A low standard deviation indicates that the data points tend to be very close to the mean; a high standard deviation indicates that the data points are spread out over a large range of values. A useful property of standard deviation is that, unlike variance, it is expressed in the same units as the data.