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    Week Probability and Statistics

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    crazytrabzonlu28
    This document discusses and provides examples of qualitative vs quantitative data and different graphs used to represent each type of data. Qualitative data is descriptive information like words, while quantitative data involves numbers. Bar graphs and pie charts are well-suited for qualitative data since they categorize information. Histograms, line graphs, and scatter plots are better for quantitative data since they show relationships between numerical values. The document also explains concepts like mean, variance, standard deviation and provides step-by-step examples of calculating them from a data set.

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    Week Probability and Statistics

    Uploaded by

    crazytrabzonlu28
    9 views17 pages
    This document discusses and provides examples of qualitative vs quantitative data and different graphs used to represent each type of data. Qualitative data is descriptive information like words, while quantitative data involves numbers. Bar graphs and pie charts are well-suited for qualitative data since they categorize information. Histograms, line graphs, and scatter plots are better for quantitative data since they show relationships between numerical values. The document also explains concepts like mean, variance, standard deviation and provides step-by-step examples of calculating them from a data set.

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    6. week Probability and Statistics

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    This document discusses and provides examples of qualitative vs quantitative data and different graphs used to represent each type of data. Qualitative data is descriptive information like words, while quantitative data involves numbers. Bar graphs and pie charts are well-suited for qualitative data since they categorize information. Histograms, line graphs, and scatter plots are better for quantitative data since they show relationships between numerical values. The document also explains concepts like mean, variance, standard deviation and provides step-by-step examples of calculating them from a data set.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    9 views17 pages

    Week Probability and Statistics

    Uploaded by

    crazytrabzonlu28
    This document discusses and provides examples of qualitative vs quantitative data and different graphs used to represent each type of data. Qualitative data is descriptive information like words, while quantitative data involves numbers. Bar graphs and pie charts are well-suited for qualitative data since they categorize information. Histograms, line graphs, and scatter plots are better for quantitative data since they show relationships between numerical values. The document also explains concepts like mean, variance, standard deviation and provides step-by-step examples of calculating them from a data set.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 17

    Qualitative vs.

    Quantitative Data

    Data is a collection of facts, such as numbers, words, measurements,


    observations or just descriptions of things.
    Data can be qualitative or quantitative.
    Qualitative data is descriptive information (it describes something)
    Quantitative data is numerical information (numbers)
    Which Graph? Why?
    1. Depends on the type of data.
    2. Depends on what you want to show.

    Graphs used for qualitative data


    Bar graph
    Circle Slice Charts (pie chart)
    Stacked graphs

    Graphs used for quantitative data


    Histogram (histogram)
    Distribution Polynomial (frequency polygon)
    Line graph
    Stem and leaf plot
    Cumulative frequency polynomial
    Box and whisker plot
    Mean standard deviation graph
    Graphs used for qualitative data

    • Good way to show relative values


    • Categorize data for good
    overview
    • Only good for discrete data, not
    for continuous data (here use
    histograms)
    • Leave space between the bars to
    show that the data are discrete to
    differentiate from a histogram plot
    Graphs used for quantitative data

    Highlight each individual outcome of e.g. a survey

    The data is grouped into “bins”


    Graphs used for quantitative data

    Good to show connections, if that is what you want


    Graphs used for quantitative data

    A scatter (XY) plot has points


    that show the relationship
    between two sets of data
    Scatter Plot – Correlation

    • When the two sets of data are strongly linked together we say they have a High
    Correlation.
    • The word Correlation is made of Co- (meaning "together"), and Relation
    • Correlation is Positive when the values increase together, and
    • Correlation is Negative when one value decreases as the other increases
    Mean, Variance and Standard Deviation

    The expected value is the probability


    multiplied by the value of each outcome
    Variance
    • Variance is the average squared deviation from the mean of a set of data.
    • It is used to find the standard deviation.
    • If measuring variance of population, denoted by 2 (“sigma-squared”).
    • Measures average squared deviation of data points from their mean.
    • Highly affected by outliers. Best for symmetric data.
    X1 X2 x
    å
    Xn

    (x - m)
    2

     2
    =
    N
    (X1 - x )2 (X2 - x )2 (Xn - x )2

    The variance is a measure that uses the mean as a point of reference.


    The variance is small when all values are close to the mean.
    The variance is large when all values are spread out from the mean.
    There are 6 fish that we caught from the lake.
    Find the variance of the length of fish.

    X (inch) (x - µ) (x - µ)2
    å (x - m)
    2
    3 -3 9
     2
    =
    4 -2 4 N
    5 -1 1
    6 0 0 σ2 = 5.66
    8 2 4
    10 4 16
    Sum 0 34
    Standard Deviation
    Standard Deviation shows the variation in data and is the square root of the variance.
    If the data is close together, the standard deviation will be small.
    If the data is spread out, the standard deviation will be large.
    Standard Deviation is often denoted by the lowercase Greek letter sigma, σ.
    Also, highly affected by outliers.

    å( x - m )
    2

    =
    N
    Variance and Standard Deviation

    x (x - µ) (x - µ)2
    å (x - m)
    2
    3 -3 9
     2
    =
    4 -2 4 N
    5 -1 1
    σ2 = 5.66
    6 0 0
    8 2 4
    σ2 = 5.66 inches2 so σ = 2.38 inches
    10 4 16
    Sum 0 34
    FIND THE VARIANCE AND STANDARD DEVIATION

    Example
    The math test scores of five students are: 92, 88, 80, 68 and 52.
    “Consider test scores values are (x)”
    3) Square the deviation from the mean:
    1) Find the Mean (x̅ ): (x -x̅ )2
    (92+88+80+68+52)/5 = 76. (16)² = 256
    (12)² = 144
    2) Find the deviation from the mean: (4)² = 16
    (x -x̅ ) (-8)² = 64
    92-76=16 (-24)² = 576
    88-76=12 4) Find the sum of the squares of the deviation from the mean
    80-76=4 (x -x̅ )2 :
    68-76= -8 256+144+16+64+576= 1056
    52-76= -24
    5) Divide by the number of data items to find the variance:
    1056/5 = 211.2

    6) Find the square root of the variance:


    Find the variance and standard deviation for the heights of the Dolphins

    70, 71, 71, 73, 74, 75, 78, 79, 79, 80

    80 5 25

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