class 03 - basic concepts of statistics and probability (1 of 2)

7/30/2019 Class 03 - Basic Concepts of Statistics and Probability (1 of 2)

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Basic Concepts of Statistics & Probability

Review ofStatisticalConcepts

DescriptiveStatistics

Numerical

andGraphicalExamples

Industrial Engineering

Statistics

Mathematical science pertaining to the collection, analysis, interpretationor explanation, and presentation of data. It produces quantities calculatedfrom a random sample taken from a population of interest

Probability

Probability is the measure of how likely an event will occur or hasoccurred. An event is one or more outcomes of an experiment .An

outcome is the result of a single trial of an experiment

The probability of event A is P(A) ; 0 P(A) 1

Statistics Probability

Probability represents uncertainty while statistics describe the sample dataor imply information from the sample data


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Numerical



Population

The entire set of potential observations (items, people, etc) about whoseproperties we would like to learn

Sample

The set of observational units (items, people, etc) whose properties ourstudy is to observe. When we select a sample by scientific randomization,we are more easily able to generalize our conclusions to the population ofinterest. For a given characteristic, the collection of measurements thatare actually observed

For practical reasons sample is used to represent the population. Data iscollected for the sample members in an observational or experimental

setting. This data can then be subjected to statistical analysis.

When we measure something in a population it is called a parameter.When we measure something in a sample it is called a statistic


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Numerical



Descriptive Statistics

Summarize the population data by describing what was observed in thesample numerically or graphically. Numerical descriptors include meanand standard deviation for continuous data types , while frequency andpercentage are more useful in terms of describing categorical data .

Inferential Statistics

Uses patterns in the sample data to draw inferences about the population.These inferences may take the form of: answering yes/no questions aboutthe data (hypothesis testing) estimating numerical characteristics of thedata (estimation), describing associations within the data (correlation),modeling relationships within the data (regression), extrapolation,

interpolation, or other modeling techniques like ANOVA, time series, anddata mining.


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Numerical



Location

The location is the expected value of the output being measured. For astable process, this is the value around which the process has stabilized.

Spread

The spread is the expected amount of variation associated with the output.This tells us the range of possible values that we would expect to see.

Shape

The shape shows how the variation is distributed about the location. Thistells us if our variation is symmetric about the mean or if it is skewed.


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NumericalandGraphicalExamples


Parameter Numerical Graphical

Location (centraltendency)

MeanMedianMode

scatter plotboxplothistogram

Spread Standard Deviationvariancerange

boxplothistogram

Shape skewnesskurtosis

Box plothistogramprobability plot


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Describing Variation

Variation in output comes from several sources such as materials,machines, methods, measurements, environment and people

Variation can be measured and described numerically or graphically

Variation means the data is distributed

Numerical Measures of Central Tendency

Knowing where the center of a distribution is tells us a lot about adistribution.

Mean, the mean, or average score, is the arithmetic center of thedistribution

Median, The median is the physical center of the distribution. It is thevalue in the middle when the values of the distribution are arrangedsequentially.

Mode The mode is the most frequent value in the distribution. It issimply the value that appears most often


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Numerical Measures of Dispersion

Measures of dispersion or variability will give us information about thespread of the scores in our distribution

Range The range is the difference between the high and low score in adistribution. Simply subtract the two numbers to find the range

Standard Deviation and Variance - both measure how far on averagescores deviate or differ from the mean. The standard deviation is the

average deviation about the mean


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Graphical Display of Central Tendency

Box PlotA graphical display that provides important quantitative informationabout a data set. Some of this information is location or centraltendency; Spread or variability; Departure from symmetry; andIdentification of outliers

HistogramA graphical display of a grouped frequency distribution as a way toabbreviate the values we are dealing with in a distribution.


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Numerical and Graphical Example





Minitab Example..

class 03 - basic concepts of statistics and probability (1 of 2)

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