Transcript Measures of Central Tendency Mean, Median, Mode, Range

Measures of
Central Tendency
Mean, Median, Mode, Range
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Curriculum Objective: The students
will determine the mean, median,
mode and range of a specific set of
data and apply these tendencies to
solving problems.
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Mean
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Data:100, 78, 65, 43, 94, 58
Mean: The sum of a collection of
data divided by the number of data
43+58+65+78+94+100=438
438÷6=73
Mean is 73
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Median
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Data:100, 78, 65, 43, 94, 58
Median: The middle number of the
set of data. If the data has an even
number of data, you add the 2
middle numbers and divide by 2.
65+78=143
143÷2=71.5
Median is 71.5
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Mode
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Data:100, 78, 65, 43, 94, 58
Mode: Number in the data that
happens most often.
No mode
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What Does It Mean to
Understand the Mean?
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We are learning the importance of
statistical concepts.
We are learning to find, use and interpret
measures of central tendency.
We will be learning the relationship of the
mean to other measures of central
tendency (mode and median)
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Properties of Arithmetic Mean
The following properties
Will be useful in understanding
The arithmetic mean and its
Relationship to the other
Measures of central tendency
Mode and Median
These principals were identified
By Strauss and Bichler
Through their research in 1988
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What Does It Mean
To Understand The Mean?
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The mean is located between the extreme
values.
The mean is influenced by values other
than the mean.
The mean does not necessarily equal one of
the values that was summed.
The mean can be a fraction.
When you calculate the mean, a value of 0,
if it appears, must be taken into account.
The mean value is representative of the
values that were averaged.
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What Would Happen If…
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You are given the following
set of Data:
1, 1, 2, 2, 2, 2, 3, 3, 4, 5
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1, 1, 2, 2, 2, 2, 3, 3, 4, 5
Determine the mean
and the median of
the given set of
numbers.
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1, 1, 2, 2, 2, 2, 3, 3, 4, 5
What happens to the
mean if a new number,
2 ,is added to the
given data? Explain
why this result occurs.
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1, 1, 2, 2, 2, 2, 3, 3, 4, 5
What happens to the
mean if a new number,
8, is added to the given
data? Explain why this
result occurs.
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1, 1, 2, 2, 2, 2, 3, 3, 4, 5
What happens to the
mean if a new number,
0, is added to the given
data? Explain why this
result occurs.
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1, 1, 2, 2, 2, 2, 3, 3, 4, 5
What happens to the
mean if two new
numbers, 2 and 3, are
added to the given
data? Explain why this
result occurs.
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1, 1, 2, 2, 2, 2, 3, 3, 4, 5
What happens to the mean if
a new number, 30, is added
to the given data? How well
does the mean represent the
new data? Can you find
another measure of central
tendency that better
represents the data?
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The Median
The median is best
describes the data
set when there is an
outlier.
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1, 1, 2, 2, 2, 2, 3, 3, 4, 5
Determine the mode
of the given set of
numbers.
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The Mode
The mode best
describes the data set
when comparing data
or when the data
includes categories
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