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

Measures of
Central Tendency
Mean, Median, Mode, Range
Standard VII-5
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
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
Mode
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Data:100, 78, 65, 43, 94, 58
Mode: Number in the data that
happens most often.
No mode
What Does It Mean to
Understand the Mean?
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In middle school we are learning the
importance of statistical concepts.
In middle school 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)
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
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.
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
1, 1, 2, 2, 2, 2, 3, 3, 4, 5
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Create a realistic
story to represent
the data.
Examples:
Number of TV
Money
Time
Number of Pets
1, 1, 2, 2, 2, 2, 3, 3, 4, 5
Determine the mean
and the median of
the given set of
numbers.
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.
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.
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.
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.
1, 1, 2, 2, 2, 2, 3, 3, 4, 5
Find two numbers that
can be added to the
given data and not
change the mean.
Explain how you chose
these two numbers.
1, 1, 2, 2, 2, 2, 3, 3, 4, 5
Find three numbers
that can be added to
the given data and not
change the mean.
Explain how you chose
these three numbers.
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?
1, 1, 2, 2, 2, 2, 3, 3, 4, 5
Find two numbers that
can be added to the
given data that change
the mean but not the
median. Explain how you
chose these two
numbers.