Download 1.4 bias and measures of central tendency

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Thursday February 10th, 2011
Thursday February 10th, 2011
Mind Buster:
Sec. 1.3 (2.4) ­ Bias in Surveys
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Sec. 1.3 ­ Bias in Surveys
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Lesson:
Sec. 1.4 (2.5)
Measures of Central Tendency
Time to practice new skills
Hand­In Your
Sec. 1.3 ­ Survey in
Bias Section
Summary
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1)
Identify the type of bias which would most likely occur in the
following scenarios and justify:
a)
A student asks a principal if he/she has ever skipped school.
b)
A group of teenagers is given a survey on gardening techniques.
c)
Belle River is surveyed on their opinion of the new border
crossing planned for the West end of Windsor.
d)
Mr. Pearce surveys how many students have completed their
homework after warning the previous day that he would be
checking homework.
2)
Identify whether the following questions are loaded, causing
potential bias or not:
a)
Do you believe the new mayor will be positive for the city?
b)
Do you eat a healthy sub for lunch or a greasy slice of pizza?
c)
Do you like Mr. Pearce as a teacher, even though he picks
favourites?
d)
Should the school have a fundraiser for the Football team?
Unit 1 ­ Statistics of One Variable
Consolidation:
Sec. 1.4 (2.5) ­ Measures of Central Tendency
Pull
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n
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n
Mean, median, and mode are considered to be measures of
central tendency due to their ability to provide a central value
which can summarize a set of data.
MEDIAN
MEAN
Most commonly known n
as the average
The middle number in n
an ordered list.
μ=Ʃx
Sample:
x=Ʃx
N
n
Tips:
• There can be multiple
modes if there are more
than one value which
occurs most often.
• odd number of values:
select middle value.
• even number of values:
take mean of middle two
values.
90 84 95 64 71 70 83 45 73 51 68
Class B 54 80 12 61 73 69
92 81 80 61 75 74 15 44 91 63 50 84
a)
Find the mean of both classes.
b)
Find the median of both classes.
Class A
45
51
55
64
66
68
70
71
12
15
44
50
54
61
61
63
• Some data sets have
no mode.
Pull
Ʃ = "Sigma"
x=
"x­b
Summation Sign
ar"
Ʃ x = Sum of all x­values
71
71
73
76
82
83
84
90
95
74
75
80
80
81
84
91
Class B
Pull
Population:
The most frequently
occurring value in a
data set.
Class A 71 82 55 76 66 71
Pull
Method:
• Arrange data set in
ascending order.
Formula:
μ=
MODE
Two classes, A and B, recently wrote the same data management
exam and had the following marks:
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69
73
92
au"
"me
c)
Find the mode of both classes.
Weighted Mean
n
Outliers
n
Some distributions of data outliers, which are values distant
from the majority of the data.
Pull
Effect of Outliers on Measures of Central Tendency
Median
Mode
Pull
Pull
Tend to drag the mean up
Have little effect on the
Have no effect in most
median since a very large cases since most outliers
or down, sometimes
significantly due to a very or very small number will be do not repeat in a data set
at the beginning or end of
large or small number
being added to the average the list in ascending order
Example:
Pull
Mean
The weighted mean is calculated in a similar manner to the mean,
except values in certain groups or categories have more
importance than others.
Example:
Sample of 7 students & their number of lates to class...
Last semester, you had an 84% going into your final
exam for English. You received a 75% on the final.
Calculate your overall average (weighted mean)
OUTLIER
Pull
Pull
1
22
22
4
5
6
8
20
Mark Category
Pull
Pull
Mean
x=4 6
Pull
Pull
1 + 2 + 2 + 4 + 5 + 6 + 8 + 20
7
8
Median = 4
4.5
Mark
%
Weighting
Factor, %
Term Work
84
70
Exam
75
30
Mode = 2
Practice: Page 133­135 #1­10, 12, 14
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