Measures of Central Tendency

1
Measures of Central Tendency

• Measures of central tendency tell us something
  about the typical-ness of a set of data.
• Tell us what the typical score is in a
  distribution of scores.
• Three measures of central tendency
• Mode
• Median
• Mean

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Measures of central tendency mode

• The mode is the score that occurs most frequently
  in a distribution.
• Sometimes more than one score occurs at
  frequencies distinctively higher than other
  scores, in which case there is(are) more than one
  mode
• Bi-modal distributions.
• Multi-modal distributions.
• Only appropriate measure of central tendency for
  nominal data.

3
Measures of central tendency median

• The median is the middle score in an ordered
  distribution of scores.
• It is the score that divides a distribution in
  half.
• It is also the score at the 50th percentile rank.
• The median is the most appropriate measure of
  central tendency for ordinal data.

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Measures of central tendency median

• In the distribution given to the right, find the
  median.
• What is the percentile rank (PR) of a score of
  13?
• What is the score cor-responding to a percentile
  rank of 15?

• Score Freq Cum. F c
• 6 2 2 3.8
• 8 5 7 13.5
• 9 0 7 13.5
• 10 8 15 28.8
• 11 11 26 50.0
• 12 9 35 67.3
• 13 6 41 78.8
• 14 4 45 86.6
• 15 5 50 96.2
• 16 2 52 100.0

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Measures of central tendency mean

• The mean is the arithmetic average value of a
  distribution (of scores).
• I Xi represents the score for individual i (in a
  distribution of size n) on the variable X, then
• ?Xi / n
• gives the mean of the distribution of X.

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Measures of central tendency mean

• For the distribution of GPAs given to the right.
  What is the mean GPA?
• Ans. 2.71

• A distribution of GPAs
• Case GPA
• 1 2.56
• 2 3.04
• 3 2.88
• 4 3.25
• 5 1.80