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STAT 110 - Section 5 Lecture 15 Professor Hao Wang University of South Carolina Spring 2012 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

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Last time: Histogram Example: Mid-term grades

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When describing a data set, the three keys are: 1.Shape 2.Center 3.Spread The histogram is one of the tools to help us with the shape.

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symmetric – the right and left sides of the histogram are approximately mirror images of each other

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Symmetric example: Human IQ

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Symmetric example: Human Height

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skewed left – the left side of the histogram (the half containing the smaller values) extends much farther than the right

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skewed left example: our mid-term grades

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skewed left example: stock returns

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skewed right – the right side of the histogram (the half with the larger values) extends much farther than the left

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skewed right example: income

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skewed right example: BMI

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unimodal – the histogram has one major spike or tall area, and the values tend to get smaller on either side of it; bimodal would be two major spikes or tall areas

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Bimodal example: old faith geyser duration of eruption

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The graph to the right is: A)Skewed Right B)Skewed Left C) Symmetric D) Bimodal E) Two of the Above

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The graph to the right is: A)Skewed Right B)Skewed Left C) Symmetric D) Bimodal E) Two of the Above

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The graph to the right is: A)Skewed Right B)Skewed Left C) Symmetric D) Bimodal E) Two of the Above

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Stemplots Test score data: 88, 90, 62, 76, 84, 89, 92, 73, 55, 76, 88, 47, 77, 93 Stemplot of Test Score Data How would you describe the distribution? 456789456789 7 5 2 3 6 6 7 4 8 8 9 0 2 3

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Stemplots When you have small data sets, stemplots are a good way to display the data. Advantages over Histograms: 1. quicker to make 2. presents more detailed information

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Stemplots To make a stemplot: 1. Separate each observation into a stem and a leaf. 2. Write the stems in a vertical column with the smallest at the top. 3. Draw a vertical line at the right of this column. 4. Write each leaf in the row to the right of its stem, in increasing order out from the stem.

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Stemplots So, what’s a stem and what’s a leaf? A stem consists of all but the final (rightmost) digit. A leaf is the final digit. Stems may have as many digits as needed. Each leaf contains only a single digit.

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Stemplots Back to our test score data set… 88, 90, 62, 76, 84, 89, 92, 73, 55, 76, 88, 47, 77, 93 1.Separate into stem and leaf. stem – 8, 9, 6, 7, 8, 8, 9, 7, 5, 7, 8, 4, 7, 9 leaf – 8, 0, 2, 6, 4, 9, 2, 3, 5, 6, 8, 7, 7, 3 2.Write stems in vertical column – 4, 5, 6, 7, 8, 9 3.Draw the vertical line. 4.Write each leaf.

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Stemplots Stemplot of Test Score Data How would you describe the distribution? 4 5 6 7 8 9 7 5 2 3 6 6 7 4 8 8 9 0 2 3

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4 5 6 7 8 9 7 5 2 3 6 6 7 4 8 8 9 0 2 3 The smallest observation in this stemplot is A)09 B)39 C)47 D)74 E)93

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4 5 6 7 8 9 7 5 2 3 6 6 7 4 8 8 9 0 2 3 This data set is A)Skewed Left B)Symmetric C)Skewed Right

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