statistic and probability

• Standard deviation measures how spread out the data points are from their mean.
• Statistics derived from the Latin word “Status” meaning state.
• Statistics refers to numbers being

  studied, data themselves, or numbers derived from the data.
• Statistics is the science of the development of applications of the most effective methods for

  planning experiments, obtaining data, and then analyzing, interpreting, and drawing conclusions

  based on the data.
• Probability is branch of mathematics that deals with uncertainty. It is a measure or estimation of

  how likely it is that an event will occur.
• Variable - an attribute that describes a person, place, thing, or idea. It is a characteristic that is

  observable or measurable in every unit of universe.
• Data collection- the process of gathering and measuring information on variables of interest, in an

  established systematic fashion that enables one to answer stated research questions, test

  hypotheses, and evaluate outcomes.
• Sample Space the set of all possible outcome.
• Event a subset of a sample space. It is also a specific collection of outcomes.
• Experiment probability is determined based on the results of an experiment repeated many times.
• Discrete Random Variable can take only finite (countable) number of distinct values. Values are

  exact and can be represented by non-negative numbers.
• Continuous Random Variable can assume an infinite number of values in an interval between two

  specific values.
• Probability Mass Function (pmf) is the probability distribution of a discrete random variable.
• A random variable is a result of chance event, that you can measure or count. It represented by

  numerical quantity that is assigned to the outcome of an experiment. It is a variable that assumes

  numerical values associated with the events of an experiment.
• Two Types of Random Variable

  Discrete Random Variable can only take a finite number of distinct values. Values are exact and represented

  by a non-negative number. While Continuous Random Variable can assume an infinite number of values

  such as measurements that can be represented by fraction, decimal and negative numbers.
• Probability Distribution of a Discrete Random Variable

  Discrete Random Variable Probability Distribution is listing all the possible values of a discrete

  random variable together with their corresponding probabilities. These values are often represented by

  tabular form, equation, and graphical form specifically Histogram.
• Mean - average of a data set, found by adding all numbers together and then dividing the sum of the

  numbers by the number of numbers It is a function that associates a real number to each element in the

  sample space.
• Variance - statistical measurement of the spread between numbers in a data set.
• Standard Deviation - statistic that measures the dispersion of a dataset relative to its mean and is

  calculated as the square root of the variance.
• The expected value of a discrete random variable X, symbolized as E(X), is often referred to as

  the long-term average or mean (symbolized as μ).
• Variance is the average of the squared differences from the mean.
• Normal Distribution – a type of data distribution that is observed in a lot of instances in real life. It

  is characterized by a bell-shaped curve with the mean, mode and median as its center and peak.
• Standard Normal Distribution – a normal distribution with a mean of 0 and a standard deviation of

  1.
• Standard normal distribution table – a compilation of areas from the standard normal distribution
• Normal distribution, also known as the Gaussian distribution, is a probability distribution that is

  symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far

  from the mean.
• Properties of a Normal Probability Distribution

  1. Distribution is a Bell shaped.

  2. Symmetrical to the center

  3. Mean, Median, and Mode coincide at the center.

  4. The curve is asymptotic to the base line.

  5. Total area is equal to 1 or 100%
• Empirical Rule, also sometimes called the three-sigma or 68-95-99.7
• Properties of a normal curve:

  • Shaded area from the given z-score up to the left side entirely, the located area in the table is the answer
  • Shaded area from the given z-score up to the right-side entirely, the located area in the table should be subtracted from 1 (absolute value)
  • Shaded area from the given z-score up to the mean/center, the located area in the table should be subtracted from 0.5 (absolute value)
  • Shaded area in between two given z-scores, the two located areas in the table should be subtracted from each other (absolute value)
• Population – data set contains all members of specified group.

  ● Sample – subset of a population

  ● Parameter – a measure or characteristics obtained by using all the data values in the population.

  ● Statistic – a measure or characteristics obtained by using only the data values in a sample.

  ● Sampling Distribution – the probability distribution for the values of the sample statistic obtained

  when random samples are repeatedly drawn from a population.