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Statistics
5/24/2017
Introduction
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Using statistics is a helpful way to
study different situations. Today I
will demonstrate how to find the
mean, median, and mode of a set
of numbers.
Topics of Discussion
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The mean (or average) is found by
taking the sum of the numbers and
then dividing by how many
numbers you added together.
The number that occurs most
frequently is the mode.
When the numbers are arranged in
numerical order, the middle one is
the median.
Topic One
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The mean (or average) is found by
adding all the numbers and then
dividing by how many numbers you
added together.
Example: 3,4,5,6,7
3+4+5+6+7= 25
25 divided by 5 = 5
The mean is 5
Topic Two
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The number that occurs most
frequently is the mode.
Example: 2,2,2,4,5,6,7,7,7,7,8
The number that occurs most
frequently is 7
The mode is 7
Topic Three
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When numbers are arranged in
numerical order, the middle one is
the median.
Example: 3,6,2,5,7
Arrange in order 2,3,5,6,7
The number in the middle is 5
The median is 5
Averaging Grades
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Lowest
55
60
75
80
80
80
83
83
93
93
93
93
93
Highest
Find The mean of the
following set of grades
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First add all the
grades together.
The total equals
1061
Now divide 1061
by 13 (total
grades
The answer is
81.61
The mean is
81.61
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Lowest
55
60
75
80
80
80
83
83
93
93
93
93
93
Highest
Find the median of the
following numbers
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The median is the
number in the
middle of
numbers which
are in order from
least to greatest.
If we count from
both sides the
number in the
middle is 83.
The median is 83
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Lowest
55
60
75
80
80
80
83
83
93
93
93
93
93
Highest
Find the mode of the
following grades
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The mode is the
number which
occurs most
often.
The number
which occurs
most often is 93
The mode is 93
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Lowest
55
60
75
80
80
80
83
83
93
93
93
93
93
Highest
Real Life
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If these were your math grades, what
would you learn by analyzing them?
The mean was 81.61. In order to raise
your grades, you would have to make
higher than an 81.61 on the rest of your
assignments.
The mode was 93 which was your
highest grade. You could look at these
papers to see why you made this grade
the most.
The median is a 83. This means that
most of your grades were higher than
your average. Find your week area and
try to improve.
Real Life
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Real Life
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Knowing the mean, median, and mode
will help you better understand the scores
on your report card. By analyzing the
data (grades) you can find your average,
the grade you received most often, and
the grade in the middle of your subject
area.
Better understanding your grades may
lead to better study habits.
Range and SD
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Range of a data set is the highest
value minus the lowest value
Q1 = lower median
Q3 = higher median
Standard deviation is the square
root of the variance
Sx=sample standard deviation
Ox=population standard deviation
Summarizing SD and
Variance
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the SD (and the variance) are
basically the same
measure of how far a set of
values (grades) differs or varies
from the mean
large SD means their student
grades scores are all over the
place
Coefficient of Variation
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Expresses the SD as a percentage
CV = standard deviation / mean * 100
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Mean and SD for
grouped data
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Computer the midpoint of each
class (if width is 1-5 then the
midpoint is 3) this is called x
Count the frequency (f) of each
class
Mean of grouped data =Sumxf/n
Weighted Average
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83(.4) + 96(.6)
.4 + .6
What is the average for a student
who has the following grades:
Project grade = 88 = 30% of avg
Test grade = 81 = 30% of avg
Quiz grade = 76 = 20% of avg
Homework = 75 = 20% of avg
Interquartile Range
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Q3-Q1
Shows the range within the inner
medians
Five-number summary
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Includes:
lowest value, Q1, median, Q2, and
highest value
Write down the following
numbers
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55
60
42
90
33
78
67
54
Compute the following
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Median and Mean
Q3 and Q1
Interquartile range
Lowest value
Highest value
Variance and Standard Deviation
of Sample