Measures of Central Tendency Mean, Median, Mode, Range

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Measures ofCentral TendencyMean, Median, Mode,
Range

• Math
• 7th Grade/Pre-Algebra

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Teacher Page

• Content Math/Pre-Algebra
• Grade Level 7 8
• Creator Mary Anne Burton
• Curriculum ObjectiveThe 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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Teacher Page

• The following activities were taken from the NCTM
  Magazine, Volume 9, Number 1, September 2003,
  Pgs 22-26.
• The students will need pencil and paper to
  complete the activities in the presentation.
• You may want students to pair share the
  activities and then share with class.

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Mean

• Data100, 78, 65, 43, 94, 58
• Mean The sum of a collection of data divided by
  the number of data
• 4358657894100438
• 438673
• Mean is 73

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Median

• Data100, 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.
• 6578143
• 143271.5
• Median is 71.5

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Mode

• Data100, 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?

• 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)

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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?

• 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

• 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

• Create a realistic story to represent the data.
• Examples
• Number of TV
• Money
• Time
• Number of Pets

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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
Find two numbers that can be added to the given
data and not change the mean. Explain how you
chose these two numbers.
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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.
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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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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.