Displaying Distributions – Quantitative VariablesFrequency PlotsDrawing Frequency PlotsExampleSlide 5Shapes of DistributionsStem-and-Leaf DisplaysSlide 8Slide 9Slide 10Splitting the NumbersSlide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Stem SplittingSlide 20Slide 21Slide 22Displaying Distributions – Quantitative VariablesLecture 15Secs. 4.4.1 – 4.4.3Mon, Feb 12, 2007Frequency PlotsFrequency PlotDrawing Frequency PlotsDraw the real line.Choose a resolution, e.g., 0.1.Mark the minimum and maximum values.Label the values on the scale, as on a ruler.Mark at regular intervals.For each data value, draw an X over that value on the scale.ExampleMake a frequency plot of the following GPAs.2.946 2.335 3.418 1.8902.731 3.855 1.344 2.1262.881 2.542 2.504 3.3671.950 2.392 2.443 3.053Frequency PlotsWhat information is conveyed by a frequency plot?Shapes of DistributionsSymmetric – The left side is a mirror image of the right side.Unimodal – A single peak, showing the most common values.Bimodal – Two peaks.Uniform – All values have equal frequency.Skewed – Stretched out more on one side than the other.Stem-and-Leaf DisplaysEach value is split into two parts: a stem and a leaf.For example, the value 1.23 could be split asstem = 123, leaf = 0, orstem = 12, leaf = 3, orstem = 1, leaf = 2, orstem = 0, leaf = 1.Stem-and-Leaf DisplaysThe stem consists of the leftmost digits of the value, as many as deemed appropriate.The leaf consists of the next digit (one digit).A note should be added indicating how to interpret the numbers.Note: 12|3 means 1.23.Stem-and-Leaf DisplaysA note should be added indicating how to interpret the numbers.Note: 12|3 means 1.23.Stem-and-Leaf DisplaysA note should be added indicating how to interpret the numbers.Note: 12|3 means 1.23.stem leaf actual valueSplitting the NumbersWe choose where to split the numbers in order to avoidToo many stems, each with too few leaves.Too few stems, each with too many leaves.Splitting the NumbersWe choose where to split the numbers in order to avoidToo many stems, each with too few leaves.Too few stems, each with too many leaves.ExampleDraw a stem and leaf display of the following GPAs.2.946 2.335 3.418 1.8902.731 3.855 1.344 2.1262.881 2.542 2.504 3.3671.950 2.392 2.443 3.053ExampleWe may split the values at the decimal point:Note: 1|2 means 1.2.1233 8 91 3 3 4 5 5 7 8 9 0 3 4 8ExampleWe may split the values at the decimal point:Note: 1|2 means 1.2.1233 8 91 3 3 4 5 5 7 8 9 0 3 4 8ExampleOr we may split the values after the first decimal place:Note: 12|3 means 1.23.13141541617181920 :95 :ExampleOr we may split the values after the first decimal place:Note: 12|3 means 1.23.13141541617181920 :95 :ExampleWhich is better?Is either one particularly good?Stem SplittingWe can obtain a good compromise (in this examle) by splitting the stems.Each stems appears twice.The first time for leaves 0 – 4.The second time for leaves 5 – 9.Stem SplittingNote: 1|2 means 1.2.11238 9 1 3 3 42335 5 7 8 90 3 48Stem SplittingNote: 1|2 means 1.2.11238 9 1 3 3 42335 5 7 8 90 3 48Shapes of DistributionsIf the distribution of household incomes were skewed to the right, what would that tell us?If a grade distribution were skewed to the left, what would that tell
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