Chapter Blueprint

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Chapter 3 The Presentation of Data Summary
Measures
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• Introduction
• Parameter (population)
• Statistic (sample)

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Measure of Central Tendency

• Some central point around which numbers tend to
  collect around
• Locates and identifies the point around which the
  data are centered

4
Measure of Dispersion

• Indicates the extent to which the individual
  observations are spread out around their center
  point
• Measures the dispersion or variability of the
  data and reflects the tendency of the individual
  observations to deviate from that center point

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Measures of Central Tendency for Ungrouped Data

• Mean (magnitude)
• Median (position)
• Mode (frequency)

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Comparing the Mean,Median, and Mode

• Mean is the most common measure of central
  tendency
• Mean is affected by extreme scores (outliers)
• Mode is less affected by extreme scores

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Measures of Dispersion

• Range
• Mean Absolute Deviation
• Variance
• Standard Deviation

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Measures of Central Tendency and Dispersion for
Grouped Data

• Mean
• Median
• Mode
• Variance
• Standard Deviation

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Other Measures of Dispersion

• Quartiles
• Deciles
• Percentiles
• Interquartile Range

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Common Uses for theStandard Deviation

• Chebyshevs Theorem
• The Empirical Rule
• Skewness
• Coefficient of Variation

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Measures of Shape Skewness
Coefficient of Skewness Zero skewness
symmetrical (mean median mode) Positive
skewness tails off to the right (mean gt
median gt mode) Negative skewness tails off to
the left (mean lt median lt mode)
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Measures of Shape Kurtosis
Coefficient of Kurtosis Mesokurtic kurtosis
3 Leptokurtic kurtosis gt
3 Platykurtic kurtosis lt 3
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The Proportion
a number that describes the frequency of
observations in a particular category as a
fraction of all observations made
Single Proprietorships 138 (p .69 or
69) Partnerships 18 (p .09 or
9) Corporations 44 (p .22 or 22) Total
Firms 200
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APPLICATION 3.1 Standard Scores
In order to make possible easy comparisons among
normal distributions of different types of
populationsbe they test scores, heights,
weights, or wagesone can convert raw data into
standard scores that indicate the number of
standard deviations between particular
observations and the mean of all observations in
a data set.
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Z X standard score F
If a distribution fits the so-called normal
curve 68.3 of all scores will fall within 1
standard deviation of the mean 95.4 of all
scores will fall within 2 standard deviations of
the mean 99.7 of all scores will fall within 3
standard deviations of the mean