DataData

Handbook Chapter 4 & 5Handbook Chapter 4 & 5

DataData

A series of readings that represents a A series of readings that represents a natural population parameter natural population parameter

It provides information about the It provides information about the population itselfpopulation itself

Organizing DataOrganizing Data

Important prelude to describing and Important prelude to describing and interpreting datainterpreting data

Charting DataCharting Data

TablesTables– Organized by rows and columnsOrganized by rows and columns

Column 1 Column 2 Column 3

Row 1

Row 2

Row 3

Charting DataCharting Data GraphsGraphs

– Organized by horizontal (abscissa) and vertical Organized by horizontal (abscissa) and vertical (ordinate) axes (ordinate) axes

Charting DataCharting Data GraphsGraphs

– Proper legendProper legend– Properly labeled axesProperly labeled axes

GraphsGraphs Multiple graphs used for comparing data should Multiple graphs used for comparing data should

map the same variables on the ordinate and map the same variables on the ordinate and abscissa and use the same scale for each graph.abscissa and use the same scale for each graph.

Describing dataDescribing data

Descriptions of data indirectly describes Descriptions of data indirectly describes actual population parametersactual population parameters

Describing the data distribution is a first Describing the data distribution is a first step in this process step in this process

Data DistributionsData Distributions

Pattern of frequencyPattern of frequency Frequency is how often a particular Frequency is how often a particular

value or set of values occurs in a data value or set of values occurs in a data setset

Histogram Frequency GraphHistogram Frequency Graph

Types of distributionsTypes of distributions

UniformUniform UnimodalUnimodal BimodalBimodal NormalNormal SkewedSkewed

UniformUniform

The distribution has an equal frequency The distribution has an equal frequency (number of occurrences) of each value (number of occurrences) of each value or category of values or category of values

Uniform Distribution of Tree Uniform Distribution of Tree HeightsHeights

Uniform Frequency Graph Uniform Frequency Graph

This is not a uniform distribution. This is not a uniform distribution.

UnimodalUnimodal

The distribution has an unequal The distribution has an unequal frequency (number of occurances) of frequency (number of occurances) of each value or category of valueseach value or category of values

The distribution has distinct central The distribution has distinct central values that have a greater frequency values that have a greater frequency than the othersthan the others

Unimodal Distribution of Tree Unimodal Distribution of Tree HeightsHeights

Unimodal Frequency GraphUnimodal Frequency Graph

SkewedSkewed

The distribution has distinct central The distribution has distinct central values that have a greater frequency values that have a greater frequency than the othersthan the others

The less frequent values are not evenly The less frequent values are not evenly distributed on either side of the high distributed on either side of the high pointpoint

Skewed Distribution of Tree Skewed Distribution of Tree HeightsHeights

Skewed Frequency GraphSkewed Frequency Graph

BimodalBimodal

The distribution has two distinct values The distribution has two distinct values or sets of values that have greater or sets of values that have greater frequencies than the others frequencies than the others

These values are separated from one These values are separated from one another by less frequent valuesanother by less frequent values

Often indicative of two populationsOften indicative of two populations

Bimodal Distribution of Tree Bimodal Distribution of Tree HeightsHeights

Bimodal Frequency GraphBimodal Frequency Graph

Two Populations of TreesTwo Populations of Trees

NormalNormal

Frequencies are equally spread out on Frequencies are equally spread out on either side of a central high pointeither side of a central high point

Bell shapedBell shaped Most frequent type of distributionMost frequent type of distribution

Normal Frequency GraphNormal Frequency Graph

Interpreting DataInterpreting Data

Descriptive statistics are used to Descriptive statistics are used to summarize datasummarize data

Several descriptive statistics are used Several descriptive statistics are used to describe two important aspects of to describe two important aspects of data distributions:data distributions:– Central TendencyCentral Tendency– DispersionDispersion

Central TendencyCentral Tendency

Most data are spread out around a Most data are spread out around a central high pointcentral high point

The central values are the ones that The central values are the ones that occur most often and thus important to occur most often and thus important to reportreport

Measures of Central Measures of Central TendencyTendency

Three common measurements Three common measurements – MeanMean

»Average valueAverage value– MedianMedian

»Center valueCenter value– ModeMode

»Most frequent valueMost frequent value

MeanMean

““Typical Value”Typical Value”

NN

Mean = Mean = XXii

i=1i=1

NN

Normal Distribution and Normal Distribution and Central MeasuresCentral Measures

In a perfectly normal distribution the In a perfectly normal distribution the mean, median and mode are all the mean, median and mode are all the samesame

Perfectly Normal DistributionPerfectly Normal Distribution

DispersionDispersion

The distribution of values that occur The distribution of values that occur less often less often

The spread of the data around the The spread of the data around the central values is important to reportcentral values is important to report

Dispersion is about the degree of Dispersion is about the degree of clustering of the dataclustering of the data

Measures of DispersionMeasures of Dispersion

Two common measurementsTwo common measurements– RangeRange

»Distance between the lowest and Distance between the lowest and highest valueshighest values

– Standard DeviationStandard Deviation»Average deviation from the meanAverage deviation from the mean

Calculate Mean and RangeCalculate Mean and Range

RangesRanges

Calculating Standard DeviationCalculating Standard Deviation

Normal Distribution and Normal Distribution and DispersionDispersion

68.26% of values fall within one 68.26% of values fall within one standard deviation on either side of the standard deviation on either side of the meanmean

95.44% of values fall within two 95.44% of values fall within two standard deviations on either side of the standard deviations on either side of the meanmean

99.74% of values fall within three 99.74% of values fall within three standard deviations on either side of the standard deviations on either side of the meanmean

Normal Distribution and Normal Distribution and Standard DeviationStandard Deviation

Graph of Graph of DispersionDispersion

Accuracy & PrecisionAccuracy & Precision

AccuracyAccuracy

ErrorError

Error = Accuracy of a particular data point Error = Accuracy of a particular data point relative to an accepted valuerelative to an accepted value

Absolute Error = Absolute Error = II Accepted – Data Accepted – Data II

Percent Error = Percent Error = II Accepted – Data Accepted – Data II x 100x 100

AcceptedAccepted

PrecisionPrecision

Precision is a measure of how Precision is a measure of how consistent the data within a data set are consistent the data within a data set are relative to each otherrelative to each other

One measure of precision of a data set One measure of precision of a data set is the standard deviation is the standard deviation SD provided that (the mean) is the accepted value (the mean) is the accepted value

++ SD SD

Calculation of SD of a Data Set Calculation of SD of a Data Set

NN

SD = SD = ––XXii

i=1i=1

N-1N-1