Math 116 1St Term (3Rd Quarter)

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Statistics

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Collection of quantitative data, also the study of how to collect and analyze

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Importance of stats

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Business economics

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Descriptive

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Methods of organizing, summarizing and presenting a mass of data so as to yield info

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Inferential

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Making generalization (predictions-guess, chance)

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Population

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Set of all individusls or entities under consideration of a study

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Individuals

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People or objects included in the study

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Data

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Body of information or observations being considered in the study

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Variable

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Characteristics of interest measurable on eafh and every individual in the universe

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Qualitative data

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Consists of categories or attributes whoch have non-numerical characteristics

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Quantitative data

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Consists of numvers representing counts or measurements

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Discrete quantitative data

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Results from either a finite number of possible values or a countable number of possible values

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Continuous quantitative data

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Results from infinitely many possible values that can be associated with points on a continuous scale

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Ungrouped data

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Data without any specific order or arrangement

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Grouped data

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Data arranged or tabulated and presented in an organized manner

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Primary data

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Information collected from original source, first hand (interviews, surveys)

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Secondary data

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Are information collected from a publishedor unpublished sources like books, newspapers, journals, theses

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Sample

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Part of the population or a sub-collection of elements drawn from the population

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Parameter

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Numerical measurement describing some characteristics of a population

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Statistic

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Numerical measurement describing some characteristics of a sample

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Survey

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Conducted tk gather opinions or feedbacks about a variety of topics

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Census survey

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Conducted by gathering information from the entire population

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Sampling survey

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Conducted by gathering information only from part of the population

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Nominal

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(Level 1) Characterized by data that consists of name, labels, or categories only (ex. Name religion address)

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Ordinal

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(Level 2) involves data that may arranged in some order, but differences between data values either cannot be determined or are meaningless. (Ex. 1. military rank 2. job position 3. year level)

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Interval

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(Level 3) like the ordinal level, with the additional property that meaningful amounts of differences between data can be determined. However, there is no inherent (natural) zero starting point. Ex. 1. IQ score 2. temperature (in 0C)

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Ratio

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(Level 4) the interval level modified to include the inherent zero starting point. For values at this level, differences and ratios are meaningful. Ex. 1. height 2. area 3. weekly allowance

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Random experiment

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• is a process or procedure, repeatable under basically the same condition"

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SAMPLE SPACE (Ω)

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• Is the set of all possible outcomes in a random experiment.

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Random variable

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(X) takes on a defined set of values with different probabilities. It is a function whose value is a real number determined by each element in the sample space.

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Expectations

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Illustrates, calculates and interpret the mean and the variance of a discrete random variable. Solves problems involving mean and variance of probability distributions.

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Expected variable

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Theoretical average of the variable

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Binomial Probability Distribution

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• A fixed number of observations, n

• A binary outcome. Generally called “success” and “failure”

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(Probability of) Success

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(Represented by) p

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(Probability of) failure

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q = 1 – p

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Normal Distribution

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Is a continuous, symmetric, bell-shaped distribution of a variable. It is sometimes called the “bell curve,” and “Gaussian curve” after the mathematician Karl Friedrich Gauss.

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Mean of distribution

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μ

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Standard deviation

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σ

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Parameters of distribution

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μ and σ

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standard normal distribution

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is a normal distribution with a mean of 0 and a standard deviation of 1.

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PROPERTIES OF THE NORMAL DISTRIBUTION

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A. A normal distribution curve is bell-shaped; denser in the center and less dense in the tails

B. The mean, median, and mode are equal and are located at the center of the distribution.

C. The curve is symmetric about the mean, which is equivalent to saying that its shape is the same on both sides of a vertical line passing through the center.

D. The curve is continuous; that is, there are no gaps or holes. For each value of X, there is a corresponding value of Y.

E. Normal distributions are defined by two parameters, the mean (μ) and the standard deviation (σ).

F. The total area under a normal distribution curve is equal to 1.00, or 100%.

G. The area under the part of a normal curve that lies within 1 standard deviation of the mean is approximately 0.68, or 68%; within 2 standard deviations, about 0.95, or 95%; and within 3 standard deviations, about 0.997, or 99.7%.