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1 Probabilistic and Statistical Techniques Lecture 3 Dr. Nader Okasha

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2 Summarizing and Graphing Data Statistical Graphics

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3 Histogram A bar graph in which the horizontal scale represents the data values and the vertical scale represents the frequencies

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4 Relative Frequency Histogram Has the same shape and horizontal scale as a histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies Relative frequency

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5 This section presents other graphs beyond histograms commonly used in statistical analysis. The main objective is to understand a data set by using a suitable graph that is effective in revealing some important characteristic.

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6 Cumulative Frequency Diagram A diagram that relates the value at the beginning of each histogram interval with the sum of all frequencies below that value. Cumulative frequency Rainfall intensity 038 0.103442 0.344946 0.517350 0.689754 0.793158 0.896562 0.93166 170

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7 Cumulative Frequency Diagram A diagram that relates the value at the beginning of each histogram interval with the sum of all frequencies below that value. Cumulative frequency Rainfall intensity 038 0.103442 0.344946 0.517350 0.689754 0.793158 0.896562 0.93166 170 Cumulative frequency Rainfall intensity

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8 Frequency Polygon Uses line segments connected to points directly above midpoint values of intervals

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9 Dot Plot Consists of a graph in which each data value is plotted as a point (or dot) along a scale of values

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10 Bar Graph A bar graph is a graphical device for depicting qualitative data. On one axis (usually the horizontal axis), we specify the labels that are used for each of the classes. A frequency, relative frequency, or percent frequency scale can be used for the other axis (usually the vertical axis). Using a bar of fixed width drawn above each interval label, we extend the height appropriately. The bars are separated to emphasize the fact that each interval is a separate category.

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11 Poor Below Average Above Average Excellent Frequency Bar Graph 1 2 3 4 5 6 7 8 9 10

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12 Stemplot (or Stem-and-Leaf Plot) Represents data by separating each value into two parts: the stem (such as the leftmost digit) and the leaf (such as the rightmost digit)

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13 Pareto Chart A bar graph for qualitative data, with the bars arranged in order according to frequencies

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14 Pie Chart A graph depicting qualitative data as slices of a pie

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15 Pie Chart The pie chart is a commonly used graphical device for presenting relative frequency distributions for qualitative data. First draw a circle; then use the relative frequencies to subdivide the circle into sectors that correspond to the relative frequency for each class. Since there are 360 degrees in a circle, a class with a relative frequency of.25 would consume.25(360) = 90 degrees of the circle.

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16 Scatter Plot (or Scatter Diagram) A plot of paired (x,y) data with a horizontal x-axis and a vertical y-axis

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