Describing DataDescribing Data

Statisticians describe a set of data in Statisticians describe a set of data in two general ways.two general ways.

– First, they compute a measure of First, they compute a measure of central tendencycentral tendency or the one number or the one number that is most typical of the entire set of that is most typical of the entire set of data.data.

– Second, they describe the Second, they describe the variationvariation, or , or spread within the data. spread within the data.

Measures of Central Measures of Central TendencyTendency

3 different measures of central 3 different measures of central tendency are available:tendency are available:– MeanMean– MedianMedian– ModeMode

– Measure of Central Tendency – the one Measure of Central Tendency – the one number that is most typical for the set number that is most typical for the set of data.of data.

Measures of Central Measures of Central TendencyTendency

Mean – the arithmetic average or the sum Mean – the arithmetic average or the sum of the individual values divided by the of the individual values divided by the number of cases.number of cases.

Median – the middle value, after all of the Median – the middle value, after all of the cases have been rank ordered from highest cases have been rank ordered from highest to lowest.to lowest.

Mode – the value of the variable that occurs Mode – the value of the variable that occurs most often.most often.

Measures of VariationMeasures of Variation

Simple measures of variation are the Simple measures of variation are the rangerange for a set of quantitative data and for a set of quantitative data and the the frequency distributionfrequency distribution for a set of for a set of qualitative data.qualitative data.

RangeRange – computed by finding the – computed by finding the difference between the smallest difference between the smallest (minimum) and the largest (maximum) (minimum) and the largest (maximum) measures of the dependent variable.measures of the dependent variable.

Frequency DistributionFrequency Distribution

The The variationvariation (qualitative data) is (qualitative data) is described through a frequency described through a frequency distribution that depicts the number distribution that depicts the number of cases falling into each category of of cases falling into each category of the variable.the variable.

– For example: For example: the leaf quality of tomatoes produced with the leaf quality of tomatoes produced with

different concentrations of chemical X.different concentrations of chemical X.

General Data Table for Descriptive General Data Table for Descriptive StatisticsStatistics

Title: The Effect of the ____________ on the Title: The Effect of the ____________ on the ____________.____________.

Descriptive Descriptive InformationInformation

Independent VariableIndependent Variable

Central Central TendencyTendency

VariationVariation

NumberNumber

Level 1 Level 2 Level 3

The Effect of Various Concentrations of Chemical X The Effect of Various Concentrations of Chemical X on the Height of Tomato Plantson the Height of Tomato Plants

Descriptive Descriptive InformationInformation

Concentration of Chemical X (%)Concentration of Chemical X (%)

0 10 20 300 10 20 30

MeanMean

RangeRange

•MaximumMaximum

•MinimumMinimum

NumberNumber

The Effect of Various Concentrations of Chemical X The Effect of Various Concentrations of Chemical X on the Health of Tomato Plantson the Health of Tomato Plants

Concentration of Chemical X (5)Concentration of Chemical X (5)

Descriptive Descriptive InformatioInformationn

00 1010 2020 3030

ModeMode

Frequency Frequency DistributioDistributionn• Healthy Healthy • UnhealthyUnhealthy

NumberNumber

The Effect of Various Concentrations of Chemical X on Leaf The Effect of Various Concentrations of Chemical X on Leaf QualityQuality

Concentration of Chemical X (%)Concentration of Chemical X (%)

Descriptive Descriptive InformatioInformationn

00 1010 2020 3030

MedianMedian

Frequency Frequency DistributioDistributionn•Quality 4Quality 4•Quality 3Quality 3•Quality 2Quality 2•Quality 1Quality 1

NumberNumber