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Chapter 1 descriptive_stats_2_rev_2009
 

Chapter 1 descriptive_stats_2_rev_2009

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    Chapter 1 descriptive_stats_2_rev_2009 Chapter 1 descriptive_stats_2_rev_2009 Presentation Transcript

    • CHAPTER 2 DESCRIPTIVE STATISTICS
      • L2 - Graphical display of Data
      • At the end of the lesson, students should be able to:
      • Construct and interpret pictorial and tabular display of data
      Learning Objectives:
    • Pictorial & Tabular Methods 1. Stem-and-Leaf Displays : How to construct a Stem-and-Leaf Display:
      • 1. Each numerical data is divided into two parts:
          • - The leading digit(s) becomes the stem,
          • and the remaining digit(s) becomes the leaf
      2. List the stem values in a vertical column. 3. Record the leaf for each observation beside its stem. 4. Write the units for stems and leaves on the display.
      • Result of Math. Exam.
      • of a 50-student class:
      • 35 42 56 41 63
      • 26 37 66 92 16
      • 49 28 56 64 72
      • 59 17 45 56 29
      • 30 45 39 37 43
      • 76 73 64 51 60
      • 40 52 57 65 83
      • 68 52 84 91 64
      • 45 76 56 90 73
      • 34 26 57 41 56
      1 6 7 2 6 6 8 9 3 0 4 5 7 7 9 4 0 1 1 2 3 5 5 5 9 5 1 2 2 6 6 6 6 7 7 9 6 0 3 4 4 4 5 6 8 7 2 3 3 6 6 8 3 4 6 9 0 1 2
      • Stem-and-Leaf Display
      Stem & Leaf Display Stem: tens digit Leaf: ones digit
    • 2. Histogram : A bar graph representing a frequency distribution of a quantitative variable.A histogram is made up of the following components. Histograms are used to summarize large data sets . Histogram: ages of 100 students Age Freq. Rel. Freq. 18 20 0.20 19 24 0.24 20 26 0.26 21 18 0.18 22 5 0.05 23 3 0.03 24 2 0.02 25 2 0.02 Sum 100 1.00 0.20 0.30 Rel. Freq.
    • 3. Box plot :
      • a graphical display that simultaneously describes several
      • important features of a data set:
        • center
        • Spread
        • departure from symmetry
        • identification of outliers
      a box plot displays the median, the first quartile and the third quartiles on a rectangular box, aligned either horizontally or vertically. sometimes called box whiskers plot.
    • HOW TO CONSTRUCT A BOX PLOT
      • Arrange the observations x 1 , …, x n in increasing order to get
      Use the following rule : Numerical Summary : Sample Median
      • LQ (Q 1 ) and UQ (Q 3 ) are defined as follows
      LOWER QUARTILE, UPPER QUARTILE, INTERQUARTILE RANGE Step 1. Arrange the values in increasing order Step 2. Q 1 is the value in position 0.25(n+1) Q 3 is the value in position 0.75(n+1) Step 3. If the positions are not integers, Q 1 and Q 3 are found by interpolation , using adjacent values
      • IQR = Q 3 – Q 1