The standard deviation of the data set 5, 5, 5, 5 is 0.
Here’s the explanation:
Standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean (average) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
In this case, all the values in the data set are the same (5). Therefore, the mean of the data set is also 5. Since there is no variation from the mean, the standard deviation is 0.
To calculate the standard deviation:
- Find the mean of the data set: (5 + 5 + 5 + 5) / 4 = 5
- Calculate the difference between each data point and the mean: 5 – 5 = 0, 5 – 5 = 0, 5 – 5 = 0, 5 – 5 = 0
- Square each difference: 0² = 0, 0² = 0, 0² = 0, 0² = 0
- Find the mean of these squared differences: (0 + 0 + 0 + 0) / 4 = 0
- Take the square root of this mean: √0 = 0
Thus, the standard deviation is 0.