Displaying Distributions Quantitative Variables Lecture 15 Secs 4 4 1 4 4 3 Mon Feb 12 2007 Frequency Plots Frequency Plot Drawing Frequency Plots Draw 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 Example Make a frequency plot of the following GPAs 2 946 2 335 3 418 1 890 2 731 3 855 1 344 2 126 2 881 2 542 2 504 3 367 1 950 2 392 2 443 3 053 Frequency Plots What information is conveyed by a frequency plot Shapes of Distributions Symmetric 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 Displays Each value is split into two parts a stem and a leaf For example the value 1 23 could be split as stem 123 leaf 0 or stem 12 leaf 3 or stem 1 leaf 2 or stem 0 leaf 1 Stem and Leaf Displays The 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 Displays A note should be added indicating how to interpret the numbers Note 12 3 means 1 23 Stem and Leaf Displays A note should be added indicating how to interpret the numbers Note 12 3 means 1 23 stem leaf actual value Splitting the Numbers We choose where to split the numbers in order to avoid Too many stems each with too few leaves Too few stems each with too many leaves Splitting the Numbers We choose where to split the numbers in order to avoid Too many stems each with too few leaves Too few stems each with too many leaves Example Draw a stem and leaf display of the following GPAs 2 946 2 335 3 418 1 890 2 731 3 855 1 344 2 126 2 881 2 542 2 504 3 367 1 950 2 392 2 443 3 053 Example We may split the values at the decimal point 1 2 3 389 133455789 0348 Note 1 2 means 1 2 Example We may split the values at the decimal point 1 2 3 389 133455789 0348 Note 1 2 means 1 2 Example Or we may split the values after the first decimal place 13 14 15 16 17 18 19 20 4 9 5 Note 12 3 means 1 23 Example Or we may split the values after the first decimal place 13 14 15 16 17 18 19 20 4 9 5 Note 12 3 means 1 23 Example Which is better Is either one particularly good Stem Splitting We 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 Splitting 1 1 2 2 3 3 3 89 1334 55789 034 8 Note 1 2 means 1 2 Stem Splitting 1 1 2 2 3 3 3 89 1334 55789 034 8 Note 1 2 means 1 2 Shapes of Distributions If 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 us
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