Statistics: Understanding Normal Curves and Sampling Distributions, Lecture notes of Social Statistics and Data Analysis

An overview of normal curves and their significance in statistics. Normal curves are symmetrical representations of naturally occurring data with a mean, median, and mode equal to each other and no skew. The concept of asymptotic properties, standard deviations, and the percentage of scores falling within specific ranges. Additionally, the document discusses the relationship between raw distributions, sampling with replacement, means of multiple samples, standard errors, and sampling distributions. The central limit theorem is also introduced, stating that as the sample size increases, the sampling distribution of means approaches a normal curve, regardless of the original distribution.

Typology: Lecture notes

2011/2012

Uploaded on 09/22/2012

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Health Statistics H391
Normal curve: visual representation of naturally occurring things.
Symmetrical
Mean=median=mode
No skew
Asymptotic: does x=/= zero
68% of scores fall between -1 and 1 standard deviations
95% fall between -2 and 2 standard deviations
Almost 98 percept fall between -3 and 3 standard deviations.
For any mean and standard deviation, there is a unique normal curve.
Raw distribution=sample distribution
Sampling w/replacement: new sample, several repeated subjects and new subjects
Means of multiple samples=sampling distributions
Each value represents an average of multiple scores from multiple samples.
Standard error: when discussing a population
Sampling distribution: distribution of a sample of means
Central limit theorem: sample size increases, sampling distribution mimics normal curve
regardless of original visual representations.

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Health Statistics H Normal curve: visual representation of naturally occurring things.

  • Symmetrical
  • Mean=median=mode
  • No skew
  • Asymptotic: does x=/= zero
  • 68% of scores fall between -1 and 1 standard deviations
  • 95% fall between -2 and 2 standard deviations
  • Almost 98 percept fall between -3 and 3 standard deviations.
  • For any mean and standard deviation, there is a unique normal curve. Raw distribution=sample distribution Sampling w/replacement: new sample, several repeated subjects and new subjects Means of multiple samples=sampling distributions
    • Each value represents an average of multiple scores from multiple samples.
    • Standard error: when discussing a population
    • Sampling distribution: distribution of a sample of means
    • Central limit theorem: sample size increases, sampling distribution mimics normal curve regardless of original visual representations.