STAT & PROB MAT102

• Variable - A characteristic or attribute that can assume different values.
• Data - The values (measurements or observations) that the variables can assume.
• Random variables - A variable whose values are determined by chance.
• Data set - A collection of data values. Each value in the data set is called a data value or a datum.
• Population - Consists of all subjects that are being studied.
• Sample - A group of subjects selected from a population.
• DESCRIPTIVE STATISTICS - Consists of the collection, organization, summarization, and presentation of data. In descriptive statistics, the statistician tries to describe a situation.
• INFERENTIAL STATISTICS - Consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions.
• Qualitative variables are variables that can be placed into distinct categories, according to some characteristic or attribute.
• Quantitative variables are numerical and can be ordered or ranked.
• Discrete variables assume values that can be counted.
• Continuous variables can assume an infinite number of values in an interval between any two specific values. They are obtained by measuring and often include fractions and decimals.
• QUALITATIVE VARIABLES: Categories, groups
• QUANTITATIVE VARIABLES: Numbers that can be ranked
• DISCRETE: Can be counted
• CONTINUOUS: Can be measured
• Nominal level of measurement classifies data into mutually exclusive (non-overlapping) categories in which no order or ranking can be imposed on the data.
• Ordinal level of measurement classifies data into categories that can be ranked; however, precise differences between the ranks do not exist.
• Interval level of measurement ranks data, and precise differences between units of measure do exist; however, there is no meaningful zero (no true zero).
• Ratio level of measurement possesses all the characteristics of interval measurement, and there exists a true zero.
• DESCRIPTIVE MEASURES allow you to characterize your data into several properties.
• MEASURE OF CENTRAL TENDENCY is a single value that represents the center point of a dataset. It helps to summarize the data and describe its main characteristics.
•  MEAN – also known as AVERAGE and the most used measure of the center.
• MEDIAN – is the score found in the middle of an arranged data set.
• MODE – the most frequently occurring score in the data set.
• Range is the difference in the maximum and minimum values of a data set.
• Variance is the expectation of the squared deviation of a random variable from its mean, and it informally measures how far a set of (random) numbers are spread out from their mean.
• Standard deviation is the most common measure of variation. It provides a numerical measure of the overall amount of variation in a data set and can be used to determine whether a particular data value is close to or far from the mean
• Experiment - a process that, when performed, results in one and only one of many observations.
• Event or Outcome - observed results of the experiment.
• Sample Space - a collection of all the possible outcomes for an experiment.

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• Random Variable - a variable whose values are determined by chance.
• DISCRETE RANDOM VARIABLE

  • A variable can assume only a specific number of values, such as the outcomes for the roll of a die or the outcomes for the toss of a coin.
• CONTINUOUS RANDOM VARIABLE

  • Variables that can assume all values in the interval between any two given values are called continuous random variables.
• Probability - a numerical measure of the likelihood that a specific event will occur.
• Property 1 - The probability of an event always lies in the range 0 to 1.
• Property 2 - The sum of the probabilities of all simple events (or final outcomes) for an experiment, denoted by ∑𝑷(𝑬𝒊), is always 1.
• A discrete probability distribution consists of the values a random variable can assume and the corresponding probabilities of the values.
• CONTINUOUS RANDOM VARIABLE

  • Variables that can assume all values in the interval between any two given values are called continuous random variables.
• Normal distribution is also known as the Gaussian distribution in honor of the German mathematician Johann Carl Friedrich Gauss (1777-1855), who derived its equation.

  Curve followed by a continuous probability distribution if it is symmetric along the mean.

  • The graph of a normal distribution is called a normal distribution curve, or simply, a normal curve.