Statistics

• mean


  is the weighted average of the possible values of the random variable x
• expected value


  is the expected value after several repetitions or trials in the statistical experiment
• parameter


  is a numerical measure that describes a population
• statistic


  is a numerical measure that describes a sample
• variance


  it is the average squared distance from the mean
• standard deviation


  the square root of the variance
• normal distribution


  is used if the data is normally distributed
• Gaussian Distribution


  normal distribution is also known as?
• Carl Friedrich Gauss


  he discovered normal distribution
• normal curve


  the bell-shaped curve of a random variable
• constructing a histogram, computing the measures of central tendency, using the central tendency theorem


  some methods you can use to check whether your data is normal or nah
• 1. each half is equal to 0.5. the area under the normal curve is 1.

  
  

  2. the mean is located at the center.

  
  

  3. the mean, median, mode, are all equal

  
  

  4. the curve is asymptotic to the x-axis

  
  

  5. the curve is unimodel

  
  

  6. the curve has inflection points

  
  

  7. the corresponding score of the mean in the normal distribution is 0

  
  

  8. the value of the population mean dictates the position of the normal curve

  
  

  9. the value of the population variance affects the spread of the normal curve

  
  

  10. the standard normal values in the x-axis reflects the number of standard deviation from the mean

  10 characteristics of normal distribution
• normal random value


  are normally distributed continuous values in their original forms such as weight, height, scores, and other continuous measurements
• standard normal value


  are the standardized scores or values wherein the mean is zero and the standard deviation is one
• probability


  is the numerical likelihood that a certain event will happen
• percentage


  converted form of probability, 0% to 100%
• percentile


  is one of the measures of position, indicating the value below the data points
• quartile, decile, parameter


  common measures of location
• case 1


  from the mean to the z-score
• case 2


  the z-scores are on the same side of the normal curve
• case 3


  the z-scores are on the different sides of the normal curve
• case 4


  the shaded region is above or below the z-score
• Stanley Smith Stevens


  proposed the levels of measurement
• nominal level


  data in this level are classified into categories
• nominal level


  Ex. Gender: Male, Female
• ordinal level


  data in this level are ranked but the degree of difference between them are not determined
• ordinal level


  ex. rank: 1st, 2nd, 3rd
• interval level


  the degree of difference between the data can be specified but not the ratio between them
• interval level


  ex. temperature in celsius scale
• ratio level


  in this level, data such as scores can be expressed as ratio
• ratio level


  ex. mass
• skewness


  is the degree of departure from the symmetry of a distribution
• karl pearson


  he made skewness
• skewed to the left or negatively skewed


  a distribution w/ longer tail on the left
• skewed to the right or positively skewed


  a distribution w/ longer tail on the right