lesson 3

• FREQUENCY DISTRIBUTION

  • an organized tabulation of the number of individuals located in different categories in different levels of measurement

  this is used to group scores together in order which would allow the researcher in a glance the set of scores
• SHAPE OF DISTRIBUTION - Normal Curve

  • a bell shaped, smooth, mathematically defined curve that is highest at its center
• Skewness


  • the nature and extent to which symmetry is absent
  • an indication of how the measurements in a distribution are distributed
• Positive Skew


  when relatively few of the scores fall at the high end of the distribution
• Negative Skew


  when relatively few of the scores fall at the low end of the distribution
• Kurtosis


  • the steepness of s distribution in its center
• MEASURES OF CENTRAL TENDENCY

  • a statistic that indicates the average or midmost score between the extreme scores in a distribution
• Arithmetic Mean


  • equal to the sum of the observations divided by the number of observations
• Median

  • the middle in a distribution
• Mode

  • the most frequently occurring score in a distribution of score
• Percentiles

  • indicate the values below which a certain percentage of the data in a data set is found
• Range

  • equal to the difference between the highest and the lowest score
• Variance

  • equal to the arithmetic mean of the squares of the differences between the scores in a distribution and their mean
• Standard Deviation

  • equal to the square root of the average squared deviations about the mean
  • equal to the square root of the variance

  symbol: σ
• STANDARD SCORE

  • a raw score that has been converted from one scale to another scale, where the latter scale has some arbitrarily set mean and standard deviation
• Z Score

  • results from the conversion of a raw score into a number indicating how many standard deviation units the raw score is below or above the mean of the distribution
  • indicates the direction and degree that any given raw score deviates from the mean of a distribution on a scale of standard deviation units
  • a z score that is positive is obtained when the raw score is greater than the mean
  • a z score that is negative is obtained when the raw score is smaller than the mean
• T Score

  
  

  • a scale with a mean set at 50 and a standard deviation set at 10
  • none of the scores in negative
  • no population, standard deviation,
  • less than 30 sample size
• THE NORMAL DISTRIBUTION

  • the mean, median, and mode are in the center of the bell curve
  • symmetrical
  • most of the test takers’ scores are close to average
  • those who scored low are located to the left tail
  • those who scored high are located to the right tail
  • it is not skewed
• SKEWNESS

  • the rule of thumb:
  • if the skewness is between -0.5 and 0.5, the data are fairly symmetrical
  • if the skewness is between -1 and -0.5 or between 0.5 and 1, the data are moderately skewed
  • if the skewness is less than -1 or greater than 1, the data are highly skewed