STAT

• Any data set can be characterized by measuring its central tendency
• Measure of central tendency


  A single value that represents a data set, to locate the center of a data set
• The most common measures of central tendency are the mean, median and mode
• Mean


  The arithmetic average, the sum of the data divided by the number of observations, the mathematical center of the distribution
• Mean


  • A set of data has only one mean
  • Mean can be applied for interval and ratio data
  • All values in the data set are included in computed the mean
  • The mean is very useful in comparing two or more data sets
  • Mean is affected by the extreme small or large values on a data set
  • The mean cannot be computed for the data in a frequency distribution with an open-ended class
  • Mean is most appropriate in symmetrical data
• Median


  The midpoint of the data array, divides the data into two equal parts
• Median


  • The median is unique
  • The median is found by arranging the set of data from lowest or highest and getting the value of the middle observation
  • Median is not affected by the extreme small or large values
  • Median can be computed for an open ended frequency distribution
  • Median can be applied for ordinal, interval and ratio data
  • Median is most appropriate in a skewed data
• Mode


  The value in a data set that appears most frequently
• Mode


  • The mode is found by locating the most frequently occurring value
  • The mode is the easiest average to compute
  • There can be more than one mode or even no mode in any given data set
  • Mode is not affected by the extreme small or large values
• Mode


  • Extreme values in a data set do not affect the mode
  • A data may not contain any mode if none of the values is "most typical"
• Properties of mode


  • The mode is found by locating the most frequently occurring value
  • The mode is the easiest average to compute
  • There can be more than one mode or even no mode in any given data set
  • Mode is not affected by the extreme small or large values
  • Mode can be applied for nominal, ordinal, interval and ratio data
• Midrange


  The average of the lowest and highest value in a data set
• Properties of midrange


  • is easy to compute
  • give the midpoint
  • is unique
  • is affected by the extreme small or large values
  • can be applied for interval and ratio data
• The midrange is greatly influenced by extreme or outlying values
• Any data set can be characterized by measuring its central tendency
• Measure of central tendency


  A single value that represents a data set, to locate the center of a data set
• The most common measures of central tendency are the mean, median and mode
• Mean


  The arithmetic average, the sum of the data divided by the number of observations, the mathematical center of the distribution
• Mean


  • A set of data has only one mean
  • Can be applied for interval and ratio data
  • All values in the data set are included in computed the mean
  • Very useful in comparing two or more data sets
  • Affected by the extreme small or large values on a data set
  • Cannot be computed for the data in a frequency distribution with an open-ended class
  • Most appropriate in symmetrical data
• Median


  The midpoint of the data array, divides the data into two equal parts
• Median


  • Unique, only one median for a set of data
  • Found by arranging the set of data from lowest or highest and getting the value of the middle observation
  • Not affected by the extreme small or large values
  • Can be computed for an open ended frequency distribution
  • Can be applied for ordinal, interval and ratio data
  • Most appropriate in a skewed data
• Mode


  The value in a data set that appears most frequently
• Mode


  • Found by locating the most frequently occurring value
  • Easiest average to compute
  • Can have more than one mode or even no mode
  • Not affected by the extreme small or large values
• Mode


  • Extreme values in a data set do not affect the mode
  • A data may not contain any mode if none of the values is "most typical"
• Properties of mode


  • The mode is found by locating the most frequently occurring value
  • The mode is the easiest average to compute
  • There can be more than one mode or even no mode in any given data set
  • Mode is not affected by the extreme small or large values
  • Mode can be applied for nominal, ordinal, interval and ratio data
• Midrange


  The average of the lowest and highest value in a data set
• Properties of midrange


  • The midrange is easy to compute
  • The midrange give the midpoint
  • The midrange is unique
  • Midrange is affected by the extreme small or large values
  • Midrange can be applied for interval and ratio data
• The midrange is greatly influenced by extreme or outlying values
• Types of Distribution


  • Symmetrical Distribution
  • Positively Skewed Distribution or Right-Skewed Distribution
  • Negatively Skewed Distribution or Left-Skewed Distribution
• Coefficient of Variation (CV)


  The standard deviation divided by the mean, expressed as a percentage
• Kurtosis is a statistical measure used to describe the distribution of observed data around the mean. It measures the peakedness or flatness of a distribution compared to the normal distribution.
• Comparing the variations of commissions and sales

  The coefficient of variation is larger for sales, so sales are more variable than commissions
• Kurtosis


  A statistical measure used to describe the distribution of observed data around the mean, measuring the relative peakedness or flatness of a distribution
• Three types of kurtosis

  • Leptokurtic (positive kurtosis, high degree of peakedness)
  • Mesokurtic (kurtosis of zero, intermediate distribution)
  • Platykurtic (negative kurtosis, low degree of peakedness)
• Simple event


  An event that includes one and only one of the outcomes
• Compound event


  A collection of more one outcome for an experiment
• Normal distribution


  Continuous probability distribution that describes data that clusters around a mean
• Normal distribution


  • Graph of the associated probability density function is bell-shaped, with a peak at the mean
  • Known as the Gaussian function or bell curve
• Normal curve developed mathematically by Abraham de Moivre


  1733
• Pierre-Simon Laplace used the normal curve to describe the distribution of errors


  1783