Standard Deviation and Variance

Even though the differences are more spread out. So let's try squaring each difference (and taking the square root at the end): √( 42 + 42 + (-4)2 + (-4)24 ) = √( 644 ) = 4 √( 72 + 12 + (-6)2 + (-2)24 ) = √( 904 ) = 4.74... That's nice! The Standard Deviation is bigger when the differences are more spread out ... just what we want. In fact this method is a similar idea to distance between points， which makes the standard deviation easy to use in other areas of mathematics. ， *Footnote: Why square the differences? If we just add up the differences from the mean ... the negatives cancel the positives: 4 + 4 − 4 − 44 = 0 So that won't work. How about we use absolute values? |4| + |4| + |−4| + |−4|4 = 4 + 4 + 4 + 44 = 4 That looks good (and is the Mean Deviation)， but what about this case: |7| + |1| + |−6| + |−2|4 = 7 + 1 + 6 + 24 = 4 Oh No! It also gives a value of 4， just applied in a different way. And it is easier to use algebra on squares and square roots than absolute values，。