Classroom Capsule 3 RoeAnn Barker

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Classroom Capsule 3RoeAnn Barker

• Description Lesson/presentation, students will
  develop an overview understanding of measures of
  central tendency
• Topic central tendencies
• Materials computer with means to project,
  whiteboard, markers, overhead transparency of
  normal distribution

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Measures of Central Tendency

• Designed for
• Blitzers Thinking Mathematically
• Author RoeAnn Barker

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Measures of Central Tendency

• Mean
• Median
• Mode
• Midrange

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Mean
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Computing the Mean

• Add the data items
• Divide your answer by the number
• of data items

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Mean for a frequency distribution
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(No Transcript)
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Median

• Arrange the data items in order, from smallest to
  largest
• If the number of data items is odd, the median is
  the item in the middle
• If the number of data items is even, the median
  is the mean of the two middle items

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Position of the Median
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Median for a Frequency Distribution
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Mode

• The data value that occurs most often in the data
• Data sets may not contain a mode
• Data sets may be bimodal

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Midrange

• lowest data value highest data value
• 2

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Measures of Dispersion

• a measure how observations in the data set are
  distributed across various categories

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Measures of Dispersion

• Range
• Standard Deviation

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Range

• Highest date value lowest data value

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Standard Deviation

• A measure of the variability of a distribution of
  data. The more the data points cluster around the
  mean, the smaller the standard deviation.

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Standard Deviation
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Computing Standard DeviationStep 1

• Find the mean of the data
• 17,18,19,20,21,22,23
• 17 18 19 20 21 22 23 140
• 7 7
• 20

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Computing Standard DeviationStep 2

• Find deviation of each item from the mean
• 20 17 3
• 20 18 2
• 20 19 1

• 20 20 0
• 20 21 -1
• 20 22 -2
• 20 23 -3

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Computing Standard DeviationStep 3

• Square each deviation

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Computing Standard DeviationStep 4

• Sum the squared deviations
• 9 4 1 0 1 4 9 28

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Computing Standard DeviationStep 5

• Divide Step 4 result by n 1 (n is the number of
  data items)

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Computing Standard DeviationStep 6

• Determine the square root of the result of the
  previous step

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OR
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Use Excel

• Tools
• Data Analysis
• Descriptive Statistics (OK)
• Input Rangehighlight the data
• check summary statistics box (OK)

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Wow !!
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• In a normal distribution, 68 of the scores fall
  within one standard deviation above and one
  standard deviation below the mean.

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Normal Distribution

• Symmetric
• Mean, median mode are the same
• Standard deviation determines the spread of the
  curve
• Mean determines the height

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Normal Distribution
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• 68 of the data falls within one standard
  deviation of the mean
• 95 of the data items fall within two standard
  deviations of the mean
• 99.7 of the data items fall within three
  standard deviations of the mean 667

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• IQ are normally distributed with a mean of 100
  and a standard deviation of 15.
• What is the IQ range of 68 of people?
• What is the IQ range of 95 of people?
• What is the IQ range of 99.7 of the people?