Measures of Central Tendency

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Measures of Central Tendency
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Measures of Central Tendency
Mean Computed from raw scores.
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Mean (Arithmetic Average) Raw Score Formula
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Measures of Central Tendency
Mean Computed from grouped scores. (A frequency
Distribution)
103.29
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Measures of Central Tendency
Mean Computed from Guessed Average
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Measures of Central Tendency
The Mean (Average)

• Advantages
• Most stable measure
• Can perform algebraic operations
• Basis for advanced statistics
• Gives us the Center of Gravity of a dist.
• Value depends on every score in dist.

• Disadvantages
• Weights extreme scores more than other measures
  of Central Tendency.

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Measures of Central Tendency
To Summarize

• Calculations for both grouped and ungrouped
  data.
• Use raw scores when possible
• Use grouped formula to calculate from freq.....
  dist. or graph.

• Guessed Average Arbitrary Origin methods are
  seldom used today, but we need to be aware of
  them.
• Raw score methods have the advantage of being
  more precise, because they use the exact value of
  every score in the distribution.
• Next we will discuss - The Median

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The Median
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Measures of Central Tendency
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Measures of Central Tendency
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Measures of Central Tendency

• Median Computed from Group Data -

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Measures of Central Tendency

• Median Computed from Group Data -

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Measures of Central Tendency

• Median Computed from Group Data -

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Measures of Central Tendency

• Median Computed from Group Data -

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Measures of Central Tendency

• Median Computed from Group Data -

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Measures of Central Tendency

• Median Computed from Group Data -

The Median
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Measures of Central Tendency
The Median ...

• Advantages
• Easy to calculate.
• Not influenced by extreme scores, so it can be
  used when we have extreme values.
• The median divides the distribution into two
  equal groups.

• Disadvantages
• It is less stable than the mean.
• The median will not permit all algebraic
  operations (addition subtraction) because we
  usually have ordinal scales

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The Mode
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Measures of Central Tendency

• The Mode
• Ungrouped Data
• The mode is the score which occurs most
  frequently.
• Grouped Data
• The mode is the midpoint of the class interval
  containing the largest number of cases.
• Estimating the Mode from the Mean and Median
• Mo 3(Mdn)-2(Mean)
• For use in skewed distributions.
• Also distributions which are bimodal.

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Measures of Central Tendency
The Mode ...

• Advantages
• Easy to calculate.
• It is most appropriate for discreet Data.
• It gives the most typical case.

• Disadvantages
• It is the least stable measure of central
  tendency.
• Different size class intervals yield different
  results
• If two non-adjacent class intervals have the same
  frequency, the distribution is bimodal and the
  mode is meaningless.
• May suggest two distributions.
• Cant perform arithmetic or algebraic expressions
  with Mo.

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Measures of Central Tendency

• Next
• Measures of Variability