03 Describing Data Graphically and Numerically Part 2

Shows points for bivariate data joint values for 2

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shows points for bivariate data (joint values for 2 quantitative variables) One variable is measured on the vertical axis and the other variable is measured on the horizontal axis 25
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Scatter Diagrams Relationship between number of commercials shown and sales: 26 Week Number of commercials Sales in $1000 1 2 50 2 5 57 3 1 41 4 3 54 5 4 54 6 1 38 7 5 63 8 3 48 9 4 59 10 2 46
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Scatter Diagrams Relationship between number of commercials shown and sales: 27
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Scatter Diagrams Relationship between number of commercials shown and sales: What type of a relationship is there between number of commercials shown and sales? Increasing Linear Relationship 28
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Scatter Diagrams Several types of relationships between two variables Increasing Linear Decreasing Linear Increasing Curvilinear Decreasing curvilinear No Relationship 29
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Bar/Pie Chart Example – CO 2 Emissions 30 Source: europa.eu
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Bar/Pie Chart Example – CO 2 Emissions 31 Source: europa.eu
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Bar/Pie Chart Example – CO 2 Emissions 32 Source: epa.gov
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Bar/Pie Chart Example – Fertility Rate 33 Source: Google public data
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Tabular and Graphical Methods for Summarizing Data Categorical Data Tabular Methods Frequency distribution Relative frequency distribution Percent frequency distribution Graphical Methods Bar chart Pie chart 34 Quantitative Data Tabular Methods Frequency distribution Relative frequency distribution Percent frequency distribution Cumulative frequency distribution Cumulative relative frequency distribution Cumulative percent frequency distribution Graphical Methods Histogram Ogive Stem and Leaf Display Line chart Scatter diagram
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Describing Data by Numerical Measures 35 Center and Location Mean Median Mode Weighted Mean N x n x x N i i n i i = = = μ = 1 1 = μ = i i i W i i i W w x w w x w X Balance point Midpoint Most often Measures of Center and Location
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Mean (Arithmetic Average) 36 The most common measure of central tendency Mean = sum of values divided by the number of values Affected by extreme values (outliers) 0 1 2 3 4 5 6 7 8 9 10 Mean = 3 0 1 2 3 4 5 6 7 8 9 10 Mean = 4 3 5 15 5 5 4 3 2 1 = = + + + + 4 5 20 5 10 4 3 2 1 = = + + + +
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The Mean is the arithmetic average of data values Population mean Sample mean Mean (Arithmetic Average) 37 n = Sample Size N = Population Size n x x x n x x n n i i + + + = = = 2 1 1 N x x x N x N N i i + + + = = μ = 2 1 1
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Median 38 In an ordered array (lowest to highest), the median is the “middle” number, i.e., the number that splits the distribution in half numerically 50% of the data is above the median, 50% is below Represented as M d The median is not affected by extreme values 0 1 2 3 4 5 6 7 8 9 10 Median = 3 0 1 2 3 4 5 6 7 8 9 10 Median = 3
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Median 39 To find the median, sort the n data values from low to high (sorted data is called a data array) Find the value in the i = (1/2) n position The i th position is the Median Index Point If i is not an integer, round up to next highest integer. (i.e., for an odd number of observations, the median is the middle value.) If i
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  • Fall '12
  • StephenD.Joyce
  • leaf diagram, Leaf Diagram Example

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