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Title: Beyond the Basics of Measures of Center
Description: This is a class lecture about Beyond the Basics of Measures of Center. You can learn about the following: • Mean from a Frequency Distribution • Weighted Mean • Skewed and Symmetric • Shape of the Distribution
Description: This is a class lecture about Beyond the Basics of Measures of Center. You can learn about the following: • Mean from a Frequency Distribution • Weighted Mean • Skewed and Symmetric • Shape of the Distribution
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BEYOND THE BASICS OF
MEASURES OF CENTER
(Class Lecture in Statistics)
Part 4
3
...
3
...
1 - 3
Example of Computing the
Mean from a Frequency
Distribution
Heights (inches) of 25 Women
67
64
65
65
64
59
67
67
72
65
64
62
66
67
66
60
70
68
61
64
60
68
65
66
62
3
...
)
Frequency distribution of heights of
women
HEIGHT
FREQUENCY
59-60
3
61-62
3
63-64
4
65-66
7
67-68
6
69-70
1
71-72
1
Class midpoints are:
59
...
5, 63
...
5, 67
...
5, 71
...
1 - 5
Example (cont
...
5) 3(61
...
5) 7(65
...
5) 1(69
...
5)
25
1621
...
86
3
...
x =
(w • x)
w
3
...
Suppose a student makes
homework/quiz average 87, exam
scores of 80 and 92, and final exam
score 85
...
3
...
10(87) 0
...
30(92) 0
...
8
1
...
1 - 9
Skewed and Symmetric
Symmetric
distribution of data is symmetric if the
left half of its histogram is roughly a
mirror image of its right half
Skewed
distribution of data is skewed if it is not
symmetric and extends more to
one
side than the other
3
...
1 - 11
Shape of the Distribution
The mean and median
cannot always be used to
identify the shape of the
distribution
...
1 - 12
Shape of the Distribution
• Consider the data:
5 5 5 5 5 10 10 10 10 10 10 15 15 15 15 15
20 20 20 20 25 25 25 30 30 30 35 35 40 45
•
Mean:
x 560
x
18
...
1 - 13
Distribution Skewed Left
•
Outliers that are much less than the median
3
...
1 - 15
Distribution Skewed Right
•
Outliers that are much more than the median
3
...
1 - 17
Title: Beyond the Basics of Measures of Center
Description: This is a class lecture about Beyond the Basics of Measures of Center. You can learn about the following: • Mean from a Frequency Distribution • Weighted Mean • Skewed and Symmetric • Shape of the Distribution
Description: This is a class lecture about Beyond the Basics of Measures of Center. You can learn about the following: • Mean from a Frequency Distribution • Weighted Mean • Skewed and Symmetric • Shape of the Distribution