A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Standard deviation is a number used to tell how measurements for a group are spread out from the average (mean or expected value). A low standard deviation means that most of the numbers are close to the average, while a high standard deviation means that the numbers are more spread out.
Standard deviation is a measure of spread that is how spread out a set of data is a low standardMoreStandard deviation is a measure of spread that is how spread out a set of data is a low standard deviation tells us that the data is closely clustered around the mean or average.
Now remember the standard deviation is a spread of the data from the mean. Now it doesn't matter ifMoreNow remember the standard deviation is a spread of the data from the mean. Now it doesn't matter if you're talking about the sample or the population.
The answer: Standard deviation is important because it tells us how spread out the values are in a given dataset.
from that image I would I would say that the SD of 5 was clustered, and the SD of 20 was definitionally not, the SD of 10 is borderline. More mathematically, The SD of 5 has 68% of the values within 10% of the range. The SD of 10 has 68% of the values within 20% of the range.