Statistics derived from the Latin word “Status” meaning state.

Statistics refers to numbers being studied, data themselves, or numbers derived from the data. It is also 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.

• 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 - the possibility of the result of any random event. It refers to determining the likelihood that any given occurrence will occur. Is a 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.

Chance refers to the “likelihood” that something will happen.

Sample Space the set of all possible outcome.

Events a subset of a sample space. It is also a specific or collection of outcomes.

Factorial or factorial function – the product of whole numbers from the given number descending to one. Fundamental Counting Principle (FCP) – the product of two or more possible outcomes to compute the total number of outcomes.

Linear Permutation – type of permutation where the object of outcome does not repeat.

Permutation with Repetition - type of permutation where the object of outcome repeats.

Combination - technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Population is any specific collection of objects of interest.

Sample is any subset or sub-collection of the population, including the case that the sample consists of the whole population, in which case it is termed a census.

Measurement is a number or attribute computed for each member of a population or of a sample.

The measurements of sample elements are collectively called the sample data.

Parameter is a number that summarizes some aspect of the population.

Statistic is a number computed from the sample data.

Descriptive statistics is the branch of statistics that involves organizing, displaying, and describing data. Inferential statistics is the branch of statistics that involves drawing conclusions about a population based on information contained in a sample taken from that population.

Qualitative data are measurements for which there is no natural numerical scale, but which consist of attributes, labels, or other non-numerical characteristics.

Quantitative data are numerical measurements that arise from a natural numerical scale.

DISCRETE – a variable which can assume finite, or at most countably infinite number of values; usually measured by counting or enumeration; data that can recounted.

CONTINUOUS – a variable which can assume infinitely many values corresponding to a line interval; values areobtained by measuring.

LEVELS OF DATA MEASUREMENT AND SCALES NOMINAL SCALE of measurement arises when we have variables that are categorical and non-numeric or where the numbers have no sense of ordering. This ischaracterized by data that consists of names, labels, or categories only.

ORDINAL SCALE also deals with categorical variables like the nominal level, but in this level ordering is important, that is the values of the variable could be ranked. – a measurement scale that ranks individuals in terms of the degree to which they possess a characteristic, but these ranks cannot be quantified or measured.

INTERVAL SCALE tells us that one unit differs by a certain amount of degree from another unit. Knowinghow much one unit differsfrom another is an additionalproperty of the interval level on top of having theproperties possess by the ordinal level. – There is no absolute zero in this scale and deals with numeric values where calculations can be made (addition, subtraction, and multiplication).

RATIO SCALE also tells us that one unit has so many times as much of the property as does another unit. Theratio level possesses a meaningful (unique and non-arbitrary) absolute, fixed zero point and allows all arithmetic operations. The existence of the zero point is the only difference between ratio and interval level ofmeasurement.

Qualitative Data – non- numeric data.

Quantitative Data – numeric data.

Primary Data – personal encounters or experiences of a person or data obtained from observation, survey, and experimentation.

Secondary Data – works or research made by other persons.

Ungrouped Data – a set or an array of things or observations whether arranged or not arranged in a particular order.

Grouped Data – data presented in a frequency distribution presentation.

Experiment is an activity that produces measurable results, called outcomes.

Sample Space is the set of all possible outcome.

Events is a subset of a sample space,and it is also a specific or collection of outcomes.

Random Variable It is a function that associates a real number to each element in the sample space. It is a result of chance in an event that you can measure or count. It is a numerical quantity that is assigned to the outcome of an experiment. It is a quantitative variable which values depends on change.

Discrete random variable - has a countable number of possible values.

Continuous random variable - can assume an infinite number of values in one or more intervals.

Probability Distribution - is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment.

Random Variable is a capacity that connects a real number with every component in the sample space. Discrete Random Variable, variables that can take on a finite number of distinct values.

Mean - considered as a measure of the `central location' of a random variable. It is the weighted average of the values that random variable X can take, with weights provided by the probability distribution.

Mean Value is the sum of the products of each possible value of a random variable and that value’s probability. Symbolically, E(X).

Variance measures of spread.

Standard Deviation is a closely related measure of variability.

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 Standard Deviation – a measure of how spread-out numbers are.

Probability density – the relationship between observations and their probability

Standard Normal Distribution A bell-shaped curve with one peak and symmetry characterizes a normal distribution. This is defined by its mean, which is the peak and center, and standard deviation, which is the offset from the center. This is the most significant distribution in terms of statistics.

Random Sampling - selecting samples from a population using chance methods or random numbersfrom the table of random numbers.

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

Statistics - a measure or characteristics obtained by using only the data values in a sample.

Sampling Distributions - the probability distribution forthe values of the sample statistic obtained when random samples are repeatedly drawn from a population.

Population refers to the whole group understudy or investigation.

Sample is a subset taken from a population, either by random sampling or by non-random sampling. Parameter is a descriptive population measure. It is a measure of the characteristics of the entire population. Statistic is the number that describes the sample. It can be calculated and observed directly.

RANDOM SAMPLING - where each point of the sample has an equal chance of being selected using the appropriate sampling technique.

Simple Random Sampling-requires using randomly generated numbers to choose a sample. More specifically, it initially requires a sampling frame,a list or database of all members of a population.

Stratified Random Sampling -It starts off by dividing a population into groups with similar attributes. Then a random sample is taken fromeach group.

Cluster Random Sampling -It starts by dividing a population into groups, or clusters. What makes this different than stratified sampling is that each cluster must be representative ofthe population. Then, you randomly select entire clusters to sample.

Systematic Random Sampling-is a very common technique in which you sample every kth element.

Lottery Sampling-is a sampling technique in which each member of the population has an equal chance of being selected. An instance of this is when members of the population have their names represented by small pieces of paperthat are then randomly mixed and picked out. In the sample, the members selected will be included.

Multi-stage Sampling-uses a combination of different sampling techniques.

Sample Means – in this table list the unique value of sample means from the previous table will be listed (if you have the same sample mean on the first table takeit as one on this table)

Frequency- count the number of sample means occuron the first sample mean table.

Probability- fraction or decimal (frequency/ the total number of possible outcomes)

*without replacement = NPn

*with replacement = N^n