Variances AddChapter 16 Day 2In chapter 4, we learned that what effect transformations had on shape, center and spread.When adding (or subtracting) a constant, only measures of position and location (mean, 1st and 3rd quartiles, etc.) change.When multiplying (or dividing) by a constant, all measures of position, location and spread change.

How are probability models affected by transformations?

Adding (or Subtracting) a ConstantThere is a correlation to how probability models behave and other measures of location, spread, etc. that you have already learned.Adding a constant will shift the mean (Expected Value), but will not affect any measure of spread standard deviation. This is the same as what you learned in Chapter 4! Please note that the shape of this distribution will not change.Multiplying (dividing) by a ConstantMore Good News!!! Multiplying by a constant will change both measures of location, and measures of spread.just as before.Also, just as before, the shape remains unaffected.To Re-Cap:

Basic Rules to Rememberacb

What if you dont have X+Y, but have X-Y instead?The equation does not change at all..you STILL add variances!!

For a more detailed explanation complete with proofs, go to the AP Central website and read an article written by our very own Mr. David Bock. The article is called Why Variances Add and Why It Matters

If this doesnt make sense to you.Think about:You mix a quart of lemonade. There should be 32 ounces, but your measuring process isnt perfectly accurate so, While 32 ounces is the expected amount, there remains some variability. You pour a 12 ounce glass. Of course that measurement is not perfect either, so its actually somewhere around 12 (give or take a little). How much is left in the pitcher?It should be around 20 ounces or so, but given the uncertainty about the initial amount and the variability in how far you filled the glass, you cant say exactly how much is left. You are less sure about the amount left because you removed an unknown amount. Subtracting some lemonade has increased the variability in the amount remaining. VARIANCES ADD! (even when you are subtracting)