1. 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)

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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=

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

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