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1) commonly means a collection of numerical facts or data
2) A science of collecting, presenting, analyzing, and interpreting numerical data
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| Organizing and summarizing numerical data in order to describe the various features of the data. |
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| Procedures and methods that can be used to make inferences (or generalization), predictions, and decisions about the population using the information contained in a sample. |
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1) commonly means a chance
2) a mathematical means of studying uncertainty, and used as a tool for inferential statistics |
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| A collection of all the elements under study (about which we are trying to draw a conclusion) or a collection of all the measurements understudy. |
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| A single member of a collection of item that we want to study |
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| A characteristic of a population unit. |
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| A numerical descriptive measure of the population |
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| A numerical descriptive measure from a sample |
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| Evaluation of each and every unit (element) in the population under study; this data contain complete (and perfect) information about the population. |
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A sample drawn such a way that each element of the population has the equal chance of being selected. Three ways of taking a simple random sample
1) draw tickets out of a hat
2) use random number tables
3) use MS Excel: FORMULA>INSERT FUNCTION>Math&TRIG>RANDBETWEEN |
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| Select every K-th item from the list |
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| Select randomly with defined strata |
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| Like a stratified sample except strata are geolgraphical regions |
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| A non-probability sampling methos that relies on the expertise of the sampler. |
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| Non numerical and categorical |
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| Assumes only specific points on a scale |
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| Assumes all values within an interval |
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| Applies to data that are divided into different categories, and these categories are used for identification purposes, e.g., female=0, male=1 |
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| Applies to data that are divided into different categories that can be ranked, e.g., bad=0, fair=1, good=2, bond ratings: AAA, AA, A, BBB, BB, National Threat Advisory: G,B,Y,O,R ect. |
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| Applies to data that can be ranked and for which the difference between two values can be calculated and interpreted, e.g., temperature, calendar time. |
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| Applies to data that can be ranked and for which the ratio between two values can be calculated and interpreted, e.g., income, weight. |
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| data arranged in ascending order or in descending order, easy to pick out extremes, typical values, and concentration of values. |
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| Partly tabular and partly graphical way of summarizaing data, and suitable for smaller data sets. |
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| A summary table in which data are arranged into conveniently established, numerically ordered class groupings or categories. The number of observations falling in each class is call the class frequency. It is a way of organizing raw data into a meaningful way |
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| =Largest observation-smallest observation |
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| Divide the range by k(sturges' rule) to determine class size. |
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| A graph made of rectangles whose areas are proportional to the relative frequencies of respective classes. |
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| A class without either a lower limit or an upper limit |
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| Another way of displaying a (relative) cumulative frequency distribution |
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| A graph of a (relative) cumulative frequency distribution. |
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| The height (y-axis) of a relative frequency histogram |
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| A circle divided into portions that represent the relative frequencies. |
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| The location at which a relative frequency distribution peaks |
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| The class that contains a mode. |
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| Measures of Central Tendency |
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| (center, location): measures the middle part of a distribution or data; these include standard deviation and range. |
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| A numerical descriptive measure computed from the population measurements (census, data) |
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| A numerical desciptive measure computed from sample measurements. |
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| Observation minus the mean. The mean is a measure of the center in the sense that it "balances" the deviations from the mean. |
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| The middle value of data when ordered from smallest to largest. |
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| The average of the largest and smallest observation |
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| The mean of data after removing the highest and lowest k percent of the observations. |
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| The n-th root of the product of n values. |
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| Geometric Mean Rate of Return |
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| An average rate of change; a good way to sort out effects that are multiplicative. |
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| The (population) variance is the average of the squared deviations from the population mean. |
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| The (sample) variance is the "average" of the squared deviations from the (sample) mean. |
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| A relative measure of the amount of variation with respect to the mean. Note the standard deviation is an absolute measure of variation. |
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| Sometimes called (z-scores) represents the signed distance from the mean measured in units of standard deviation. |
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For any sample or population data the proportion of observations that lie within k standard deviations from the mean is at least 1-1/ksquared.
This describes the distribution of data using the mean and the standard deviation together. |
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When the distribution of (smaple or population) data is approximately bell shaped(or mound-shaped), then
approximately 68% of the data are within 1 standard deviation from the mean,
approximately 95% of the data are within 2 standard deviation from the mean, and
aproximately 99% of the data are within 3 standard deviation from the mean. |
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| Extreme observations not conforming to the rest of the observation. As a rule of thumb observations that are three standard deviation above or below the mean are considered as outliers. |
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| also called lower quartile, and denoted by Q1, is the 25th percentile. |
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| Also called upper quartile and denoted by Q3, is the 75th percentile. |
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| Q3-Q1, and is a measure of variability. |
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| (Q1+Q3)/2, a measure of location |
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| a graphical method of displaying the quartiles, ranges, and extreme values of data. In a box plot the left "I" (also called the left hinge) is at Q1, the right "I" (right hinge) at Q3, and "I" inside of the box is at the median, the right (left) whisker extends out from the right (left) hinge to the largest(smallest) observation with 1.5 IQR above (below) the right (left) hinge, observations beyond the reach of the whiskers are considered outlying observation. |
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1) commonly means a chance
2) a mathematical means of studying uncertainty, and used as a tool for inferential statistics. |
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| Any activity from which an outcome, measurement, observation, or result is obtained, and outcomes cannot be predicted with certainty. |
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| Basic outcome (elementary outcome) |
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| Each possible outcome of a random experiment. |
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| The set of all possible basic outcomes, usually denoted by S. |
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| A subset of the sample space, usually denoted by A,B,C,.... |
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| If any one of the basic outcomes in the event occurs. |
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| A simple event (elementary event) |
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an event with only one basic outcome, usually denoted by Ei.
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| Two events. if one and only one of them occur. |
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| every possible outcome of an experiment is assumed to be equally likely, known a priori by natire of the experiment. |
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| (relative frequency method): the probablilty of an outcome is the relative frequency of the outcome, that is, the frequency of occurrences of the outcome divided by the number of trials repeated. |
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| The probability of an event relects a person's degree of belief that the event will occur based on experience, intuitive judgement, or expertise. |
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An event A, denoted by A' consists of all basic outcomes in S that do not belong to A.
P(A)=1-P(A') |
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Intersection
(Joint Probability) |
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| Two events A and B, denoted by A ^ B or AB consists of all basic outcomes that belong to both A and B. The probability of the intersection of two events, denoted by P(AB) |
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| Two events A and B, denoted by P(A union B) consists of all basic outcomes that belong to either A or B or both. |
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| P(A union B)=P(A)+P(B)-P(A^B) |
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A given that B has occured is denoted by A|B, and its probabilit is
P(A|B)=P(A^B)/P(B) |
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| The probability that an observation will show any single specific characteristic and is obtained by summing the appropriate joint probabilities over all values of other variables. |
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P(A^B)=P(A)P(B|A)
P(A^B)=P(B)P(A|B) |
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If and only if one of the following holds:
1) P(A|B)=P(A) when P(B) does not =0
2) P(B|A)=P(B) when P(A) does not =0
3) P(A^B)=P(A)P(B) |
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