how do you interpret the standard deviation , when you have only the mean, and standard...
deviation, for example the standard deviation is 30.4 and the mean is 24.8,
standard deviation tells you how close the various data points are to the mean - a high standard deviation means the data is spread out, a low standard deviation means most the data is fairly close to the mean.
So if all the data is the same value, the standard deviation is zero.
1 standard deviation from the mean in either direction accounts for around 68 percent of data. 95% of data is within 2 standard deviations of the mean and 3 standard deviations accounts for 99% of data.
i.e 68% of your data is between -5.2 and 62.4
The higher the standard deviation around the mean the more the heterogeneity in the sample. If you mix some very poor and some very rich guys and calculate the SD and mean it will be quite high. But keep the rich in the rich group and the poor in the poor group, the difference between the two means will be high and significant but the SD of each sample will be less than the mixed sample.
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