displaying distributions with displaying distributions with graphs october 22, 2012 exploratory data

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  • Displaying Distributions with

    Graphs

    October 22, 2012

    Exploratory Data Analysis

    Qualitative Variables

    Quantitative Variables

  • 1.0 Exploratory Data Analysis

    Here we analyze the data on its’ own terms. no extraneous assumptions

    The idea is to organize and summarize so as to uncover any underlying features of the data.

    Our focus is on the distribution of the variables.

    Definition The distribution of a variable tells us what values it takes and how often it takes these values.

  • 2.0 Qualitative Variable

    Pie Charts: shows how often the different values occur by wedges of a circle.

    Bar Graphs: shows how often the different values occur by bars.

  • 2.1 Mystery Question

    1 2%

    2 5% 3

    9%

    4 10%

    5 21%6

    14%

    7 19%

    8 6%

    9 8%

    10 6%

    Pie Chart

    0

    2

    4

    6

    8

    10

    12

    14

    16

    18

    20

    1 2 3 4 5 6 7 8 9 10 11

    Series1

    How nervous are you about taking STAT 220? (1=very nervous; 10=not at all)

  • 2.2 Sex Bias at U.C. Berkeley?

    A or B

    7%

    C, D, E, F 93%

    What Majors do Women Pick?

    A or B 52%

    C, D, E, F 48%

    What Majors do Men Pick?

  • 3.0 Quantitative Variables

    Stem and Leaf Plots.

    Histograms.

  • 3.1 Mystery Question

    35 40 60 32 55 38 32 45 37 40 35 37 40 35 74 47 27 31 48 32 30 28 30 45 44 28 27 30 38 37 34 40 30 33 45 31 38 34 35 35 25 50 45 36 60 40 45 39 33 33 38 35 30 35 37 45 50 36 10 26 42 52 30 35 16 55 45 37 29 35 40 48 45 40 13

    1 2 3 4 5 6 7

    1 0 6 3 2 8 8 7 7 5 6 9 3 5 2 8 2 7 5 7 5 1 2 0 0 0 8 7 4 0 3 1 8 4 5 5 6 9 3 3 8 5 0 5 7 6 0 5 7 5 4 0 5 0 0 7 8 5 4 4 0 5 5 0 5 5 2 5 0 8 5 0 5 5 0 0 5 6 0 0 7 4

    (a) (b)

    1 | 036 2 | 5677889 3 | 0000001122233344555555555667777788889 4 | 00000002455555555788 5 | 00255 6 | 00 7 | 4

    (c) stem

    leaves

    Stem and Leaf Plot

    How old is Prof. Grove?

  • 3.1 Mystery Question

    35 40 60 32 55 38 32 45 37 40 35 37 40 35 74 47 27 31 48 32 30 28 30 45 44 28 27 30 38 37 34 40 30 33 45 31 38 34 35 35 25 50 45 36 60 40 45 39 33 33 38 35 30 35 37 45 50 36 10 26 42 52 30 35 16 55 45 37 29 35 40 48 45 40 13

    Age (years) 10 20 30 40 50 60 70 80

    (a)

    (b)

    How old is Prof. Grove?

  • 3.2 Basic Shapes of a Histogram

  • 3.3 What to Look For in a

    Distribution

    Detect outliers, if any.

    Look at the shape. I Is it symmetric? skewed?

    Where is it centered? Where is the mid-point?

    How spread out is it?

  • 4.0 Example

    Mystery Question: What was your Math S.A.T. score?

    1 2

    5

    7

    10

    16

    11

    7

    n=59

    Shape?

    Center?

    Spread?

  • 4.1 Example

    Mystery Question: How many years in WA state?

    Shape?

    Center?

    Spread?

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