2-3B-Weighted Mean Mean of data with varying weights. x = Σ(x∙w)/Σw Multiply each entry by its weight(decimal) A weight of 60% is multiplied by .60 ADD up these values DIVIDE by the sum of the weights (1)

Example: find the weighted mean Your grade in a class is determined by the following values: Test mean- 50%, midterm – 15%, final exam-20%, labs-10%, homework-5% Source Score, x Weight, w xw Test mean 86 Midterm 96 Final 82 Labs 98 Homework 100

Example: find the weighted mean Your grade in a class is determined by the following values: Test mean- 50%, midterm – 15%, final exam-20%, labs-10%, homework-5% Source Score, x Weight, w xw Test mean 86 .5 Midterm 96 Final 82 Labs 98 Homework 100

Example: find the weighted mean Your grade in a class is determined by the following values: Test mean- 50%, midterm – 15%, final exam-20%, labs-10%, homework-5% Source Score, x Weight, w xw Test mean 86 .5 Midterm 96 .15 Final 82 .20 Labs 98 .10 Homework 100 .05 Σw=1

Example: find the weighted mean Your grade in a class is determined by the following values: Test mean- 50%, midterm – 15%, final exam-20%, labs-10%, homework-5% Source Score, x Weight, w xw Test mean 86 .5 43 Midterm 96 .15 Final 82 .20 Labs 98 .10 Homework 100 .05 Σw=1

Example: find the weighted mean Your grade in a class is determined by the following values: Test mean- 50%, midterm – 15%, final exam-20%, labs-10%, homework-5% Source Score, x Weight, w xw Test mean 86 .5 43 Midterm 96 .15 14.4 Final 82 .20 16.4 Labs 98 .10 9.8 Homework 100 .05 5 Σw=1 Σ(xw)=88.6

Frequency Distribution Mean 1) Find midpoint of each class x = (lower limit + upper limit)/2 2) multiply each midpoint & frequency and ADD them all up (sum) Σ(x∙f) 3) Find SUM of frequencies, n = (Σf) 4) Find the MEAN of the frequency distrib. x=Σ(x∙f)/n

Example: Find mean number of minutes spent online. Class Frequency Midpoint (x·f) 7-18 6 19-30 10 31-42 13 43-54 8 55-66 5 67-78 79-90 2 Σ=n=

Example: Find mean number of minutes spent online. Class Frequency Midpoint (x·f) 7-18 6 19-30 10 31-42 13 43-54 8 55-66 5 67-78 79-90 2 Σ=n=50

Example: Find mean number of minutes spent online. Class Frequency Midpoint (x·f) 7-18 6 (7+18)/2=12.5 19-30 10 31-42 13 43-54 8 55-66 5 67-78 79-90 2 Σ=n=50

Example: Find mean number of minutes spent online. Class Frequency Midpoint (x·f) 7-18 6 (7+18)/2=12.5 19-30 10 24.5 31-42 13 36.5 43-54 8 48.5 55-66 5 60.5 67-78 72.5 79-90 2 84.5 Σ=n=50

Example: Find mean number of minutes spent online. Class Frequency Midpoint (x·f) 7-18 6 (7+18)/2=12.5 12.5∙6=75 19-30 10 24.5 31-42 13 36.5 43-54 8 48.5 55-66 5 60.5 67-78 72.5 79-90 2 84.5 Σ=n=50

Example: Find mean number of minutes spent online. Class Frequency Midpoint (x·f) 7-18 6 (7+18)/2=12.5 12.5∙6=75 19-30 10 24.5 245 31-42 13 36.5 474.5 43-54 8 48.5 388 55-66 5 60.5 302.5 67-78 72.5 435 79-90 2 84.5 169 Σ=n=50 Σ=2089 X = Σ(x·f)/n = 2089/50 = 41.8 minutes

Shape of Distributions 1. Symmetric: left & right same: Mean, median, mode SAME & in middle 2. Uniform or Rectangular: equal frequencies Also Symmetric: mean median & mode same 3. Skewed: one side elongates more than other Skewed left: negatively: tail on left mean, median, mode Skewed right: positively: tail on right mode, median, mean

Distribution Examples: Symmetric Uniform (rectangular) Skewed - left Skewed-right