Chapter 2: Describing Location In a Distribution

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Chapter 2 Describing LocationIn a Distribution

• Section 2.1
• Measures of Relative Standing
• And Density Curves

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Case Study

• Read page 113 in your textbook

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Where are we headed?
Last Chapter
Analyzed a set of observations graphically and
numerically
This Chapter
Consider individual observations
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Consider this data set

• 6 7
• 7 2334
• 7 5777899
• 8 00123334
• 8 569
• 9 03

How good is this score relative to the others?
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Measuring Relative Standing z-scores

• Standardizing converting scores from the
  original values to standard deviation units

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Measuring Relative Standingz-scores
A z-score tells us how many standard deviations
away from the mean the original observation
falls, and in which direction.
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Practice Lets Do p. 118 1
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Measuring Relative StandingPercentiles

• Norman got a 72 on the test. Only 2 of the 25
  test scores in the class are at or below his.
• His percentile is 2/25 0.08, or 8. So he
  scores in the 8th percentile.

6 7 7 2334 7 5777899 8 00123334 8 569 9 03
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Density Curves
Mathematical Model For the Distribution
Histogram of the scores of all 947 seventh-grade
students in Gary, Indiana.

• The histogram is
• Symmetric
• Both tails fall off smoothly from a single center
  peak
• There are no large gaps
• There are no obvious outliers

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Density Curves
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Density Curves Normal Curve
This curve is an example of a NORMAL CURVE. More
to come later.
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Describing Density Curves

• Our measure of center and spread apply to density
  curves as well as to actual sets of observations.

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Proportions in a Density Curve
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Describing Density Curves

• MEDIAN OF A DENSITY CURVE
• The equal-areas point
• The point with half the area under the curve to
  its left and the remaining half of the area to
  its right

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Describing Density Curves

• MEAN OF A DENSITY CURVE
• The balance point
• The point at which the curve would balance if
  made of solid material

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Mean of a Density Curve
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Notation
Usually

• Use English letters for statistics
• Measures on a data set
• x mean
• s standard deviation
• Use Greek letters for parameters
• Measures on an idealized distribution
• µ mean
• s standard deviation