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Algebra ACE Summation Notation & Mean Absolute Deviation – MAD I. Name: ___________________ Summation Notation A mathematical representation for ______________ elements of a __________ _________. Summation Notation is also called ______________ ___________, the after the capital Greek letter. It looks like this: n To represent the process of adding a set of data elements we write: where x i 1 i xi represents a _________ ____________ “index” i represents its ____________ in that set of data. “n” represents the __________ __________ of elements in the data. The Jones family has 6 members (including Fluffy and Spot), so n = 6. Their heights the elements of our data set. Member Height Data set is {65, 72, 70, 58, 22, 28} Mom Dad Bobby Joey Fluffy Spot 65” 72” 70” 58” 22” 28” So, x1 = 64 x2 = 72 x3 = 70 x4 = 58 x5 = 22 x6 = 28 ________ or “mu” is our new symbol for mean (average). It is also a Greek letter. Now our formula for finding the mean looks like this: Find for the Jones family heights. = _____________ inches. Write the formula here: Algebra ACE II. Mean Absolute Deviation (MAD) Mean Absolute Deviation is a way to determine the _____________ or ________________ of a set of data. When we calculate the MAD, we can use it to give is a general idea of what is considered “normal” for that particular set of data. MAD is often preferred by statisticians over its cousin ____________ ________________ because it is less affected by ________________. The formula for Mean Absolute Deviation: 𝑛 MAD = ∑𝑖=1 |𝑥𝑖 −𝜇| 𝑛 Step 1: Find the ______________. Step 2: ________________ the mean from each element in the data set. Step 3: Write down the ________________ ___________ for each of those differences. Step 4: ____________ those numbers. Step 5: ____________________ that sum by n (the number of elements in the data set) Complete each step for our set of data. Jones family heights = {65, 72, 70, 58, 22, 28} Step 1: Step 2: Step 3: Step 4: Step 5: MAD = What does the MAD tell us about the heights of the Jones family? __________________________________________________________________ __________________________________________________________________