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# Chapter 1 descriptive_stats_2_rev_2009

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### Chapter 1 descriptive_stats_2_rev_2009

1. 1. CHAPTER 2 DESCRIPTIVE STATISTICS <ul><li>L2 - Graphical display of Data </li></ul>
2. 2. <ul><li>At the end of the lesson, students should be able to: </li></ul><ul><li>Construct and interpret pictorial and tabular display of data </li></ul>Learning Objectives:
3. 3. Pictorial & Tabular Methods 1. Stem-and-Leaf Displays : How to construct a Stem-and-Leaf Display: <ul><li>1. Each numerical data is divided into two parts: </li></ul><ul><ul><ul><li>- The leading digit(s) becomes the stem, </li></ul></ul></ul><ul><ul><ul><li>and the remaining digit(s) becomes the leaf </li></ul></ul></ul>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.
4. 4. <ul><li>Result of Math. Exam. </li></ul><ul><li>of a 50-student class: </li></ul><ul><li>35 42 56 41 63 </li></ul><ul><li>26 37 66 92 16 </li></ul><ul><li>49 28 56 64 72 </li></ul><ul><li>59 17 45 56 29 </li></ul><ul><li>30 45 39 37 43 </li></ul><ul><li>76 73 64 51 60 </li></ul><ul><li>40 52 57 65 83 </li></ul><ul><li>68 52 84 91 64 </li></ul><ul><li>45 76 56 90 73 </li></ul><ul><li>34 26 57 41 56 </li></ul>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 <ul><li>Stem-and-Leaf Display </li></ul>Stem & Leaf Display Stem: tens digit Leaf: ones digit
5. 5. 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.
6. 6. 3. Box plot : <ul><li>a graphical display that simultaneously describes several </li></ul><ul><li>important features of a data set: </li></ul><ul><ul><li>center </li></ul></ul><ul><ul><li>Spread </li></ul></ul><ul><ul><li>departure from symmetry </li></ul></ul><ul><ul><li>identification of outliers </li></ul></ul>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.
7. 7. HOW TO CONSTRUCT A BOX PLOT
8. 8. <ul><li>Arrange the observations x 1 , …, x n in increasing order to get </li></ul>Use the following rule : Numerical Summary : Sample Median
9. 9. <ul><li>LQ (Q 1 ) and UQ (Q 3 ) are defined as follows </li></ul>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 <ul><li>IQR = Q 3 – Q 1 </li></ul>