Statistics and probability

• Statistics


  It deals with the collection, organization and presentation, analysis, and interpretation
• Types of statistics


  • Descriptive statistics - it is a group of statistical measurements that aims to provide the basic characteristics of a data set
  • Inferential statistics - it aims to infer or make interpretation by making a concluding statement about the population bases on the result derives from data set
• Data


  A body of information or observations being considered by the researcher
• Information


  The basis for decision making is produced
• Variable


  It is used to define certain observable values of characteristics
• Types of variables


  • Qualitative variables - Are categorical characteristics
  • Quantitative variables - Have actual value
• Quantitative variables


  • Discrete variable - Data can be counted with finite or infinite number of value. No decimal or whole numbers
  • Continuous variables - Can be measured and the possible values are infinite. Have decimal
• Measure of central tendencies


  An estimate of center of a distribution of values
• Mean


  Arithmetic mean is computed as the sum of all observation divided by the number of observations. Also called the average
• Median


  The middle value in a array of observations or simply the midpoint of an array of numbers
• Mode


  It is the most frequently occurring value of a measure in a data set
• Levels of measurement


  • Nominal - no sense of order or rank
  • Ordinal - Order is important. Variables could be ranked
  • Interval - Level shows that one unit differs by a certain amount of degree from another unit
  • Ratio - Level shows that one unit has so many times as much of the property does another unit
• Probability


  It deals with the occurrence of a random event
• Outcome


  The result of a single trial of a probability experiment
• Sample space


  A collection or a set of possible outcomes of a random experiment
• Random Variable


  A variable whose possible values are numerical outcomes of a random phenomenon. Denoted by x
• Discrete probability distribution


  It consists of the values a random variable can assume and the corresponding probabilities of the values. The probabilities are determined theoretically or by observation
• Frequency distribution table


  A way to organize data so that it makes the data more meaningful. A count of how often something happened
• Normal Distribution


  A continuous probability distribution that describes data that cluster around a mean. It describes how the values of variables are distributed
• Properties of a normal distribution

  • The distribution is bell-shaped
  • The mean, median, and mode are equal and are located at the center of the distribution
  • The normal distribution is unimodal
  • The normal distribution curve is symmetrical around the mean
  • The normal distribution is continuous
  • The normal distribution is asymptotic
  • The total area under the normal distribution curve is 1.00 or 100%
  • The area under the part of a normal curve that lies within 1 standard deviation of the mean is 68%, within 2 standard deviation is about 95%; and with 3 standard deviation is about 99.7%
• Z-DISTRIBUTION

  A normal distribution can be converted into a STANDARD NORMAL DISTRIBUTION by obtaining z-score
• Standard deviation


  Measure how spread out the values are in a data set
• Measures of Dispersion


  • Range, interquartile range, variance, and standard deviation
• Range


  Difference between the highest and the lowest value