# Describing Data Statisticians describe a set of data in two general ways. Statisticians describe a set of data in two general ways. –First, they compute.

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Describing Data Statisticians describe a set of data in two general ways. Statisticians describe a set of data in two general ways. –First, they compute a measure of central tendency or the one number that is most typical of the entire set of data. –Second, they describe the variation, or spread within the data.

Measures of Central Tendency 3 different measures of central tendency are available: 3 different measures of central tendency are available: –Mean –Median –Mode –Measure of Central Tendency – the one number that is most typical for the set of data.

Measures of Central Tendency Mean – the arithmetic average or the sum of the individual values divided by the number of cases. Mean – the arithmetic average or the sum of the individual values divided by the number of cases. Median – the middle value, after all of the cases have been rank ordered from highest to lowest. Median – the middle value, after all of the cases have been rank ordered from highest to lowest. Mode – the value of the variable that occurs most often. Mode – the value of the variable that occurs most often.

Measures of Variation Simple measures of variation are the range for a set of quantitative data and the frequency distribution for a set of qualitative data. Simple measures of variation are the range for a set of quantitative data and the frequency distribution for a set of qualitative data. Range – computed by finding the difference between the smallest (minimum) and the largest (maximum) measures of the dependent variable. Range – computed by finding the difference between the smallest (minimum) and the largest (maximum) measures of the dependent variable.

Frequency Distribution The variation (qualitative data) is described through a frequency distribution that depicts the number of cases falling into each category of the variable. The variation (qualitative data) is described through a frequency distribution that depicts the number of cases falling into each category of the variable. –For example:  the leaf quality of tomatoes produced with different concentrations of chemical X.

General Data Table for Descriptive Statistics Title: The Effect of the ____________ on the ____________. Descriptive Information Independent Variable Central Tendency Variation Number Level 1 Level 2 Level 3

The Effect of Various Concentrations of Chemical X on the Height of Tomato Plants Descriptive Information Concentration of Chemical X (%) 0 10 20 30 Mean Range Maximum Maximum Minimum Minimum Number

The Effect of Various Concentrations of Chemical X on the Health of Tomato Plants Concentration of Chemical X (5) Descriptive Information 0 10 10 20 20 30 30 Mode Frequency Distribution Healthy Healthy Unhealthy Unhealthy Number

The Effect of Various Concentrations of Chemical X on Leaf Quality Concentration of Chemical X (%) Descriptive Information 0 10 10 20 20 30 30 Median Frequency Distribution Quality 4 Quality 4 Quality 3 Quality 3 Quality 2 Quality 2 Quality 1 Quality 1 Number

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