But remember, by squaring the differences, we get a wider spread between the differences, which is called higher weighting. Thanks to Lura Ercolano for clearing my misconception about using absolute value to get the variance. Q2) I think we could use the absolute value,but for the official definition, you have to square the differences. Therefore, the difference between Variance and the Standard Difference is that the Variance is 'The average of the squared differences from the Mean' and the Standard Deviation is it's square-root. And of course, you will see the same when you have endured the boring process of calculating the Variance and then the Standard Deviation. You can see clearly that the data-points are grouped closely together more in the first set than the second set of data-points. The smaller the Standard Deviation, the closely grouped the data point are. Standard Deviation is the measure of how far a typical value in the set is from the average.

Basically, it is the square-root of the Variance (the mean of the differences between the data points and the average). Q1) The Standard Deviation is the 'mean of mean'.

Statistics by khan academy