Aim: What are the properties of a normal distribution

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Aim What are the properties of a normal
distribution?
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Do Now

• What type of curve is preferred? Why?
• Symmetric
• Skewed Right
• Skewed Left

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What is a normal distribution?

• A graphical representation that generates a
  bell-shaped curve that is symmetrical is known as
  a normal distribution.

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Where do the measures of central tendency fit on
the normal curve?

• By definition, a normal distribution is
  symmetrical therefore, the mean, median and mode
  are all found at the same positionat the center
  of the distribution.
• The normal curve is unimodal (has only one mode
  one peak)

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MEANMODEMEDIAN
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Who do we talk about with a normal distribution?

• For the majority, we use normal distribution to
  describe a population.
• FYI Descriptive measures of population are
  parameters.

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What is the mathematical equation for the normal
curve?

• The mathematical equation for a normal
  distribution is
• A
• A
• A population mean
• population standard deviation

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What are important aspects of a normal
distribution?

• The area under the normal distribution curve is
  more important than the frequencies.
• The shape and size of the normal distribution
  curve depends on two parameters the mean and the
  standard deviation.

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Same mean but different SD

• The larger the standard deviation, the more
  disperse, or spread out, the distribution is.

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Different means but same SD

• These curves have the same shape but are located
  at different positions on the x-axis.

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How do we look at the IQR in a distribution?

• Reminders
• The Median is the 50th percentile of a
  distribution (half)
• The first quartile is the 25th percentile of a
  distribution (half way between minimum and
  median)
• The third quartile is the 75th percentile of a
  distribution (half way between median and maximum)

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How do we look at the IQR in a distribution?

• The pth percentile of the data set is a
  measurement such that after the data are ordered
  from smallest to largest, at most p of the data
  are below this value and at most (100-p) above
  it.

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How do we look at the IQR in a distribution?

• Thus, the median is the 50th percentile.
• Also, Q1 lower quartile 25th percentile and
  Q3 upper quartile 75th percentile.

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Summary of the Properties of the Theoretical
Normal Distribution

• Normal Distribution is a continuous, symmetric,
  bell shaped distribution of a variable.
• The mean, median and mode are equal and located
  at the center of the distribution.
• Curve never touches the x-axis but gets
  increasingly closer.