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Lec_2_Notes[1] stats 10 - DESCRIBING DISTRIBUTIONS...

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1 DESCRIBING DISTRIBUTIONS NUMERICALLY
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2 Numerical Summaries Mean Median Mode Describing Data Numerically Variance Standard Deviation Range Interquartile Range Central Tendency Variation
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3 Central Tendency Mean Median Mode n x x n 1 i i ! = = Midpoint of ranked values Most frequently observed value Arithmetic average Measures of center: Mode, Median, Mean
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4 Measures of Center: Mode • A measure of central tendency • Value that occurs most often • Not affected by extreme values • Used for either numerical or categorical data • There may be no mode • There may be several modes 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mode = 9 0 1 2 3 4 5 6 No Mode
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5 In an ordered list, the median is the “middle” number (50% above, 50% below) • Not affected by extreme values 0 1 2 3 4 5 6 7 8 9 10 Median = 3 0 1 2 3 4 5 6 7 8 9 10 Median = 3 Measures of Center: Median
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6 Measures of Center: Median The Median the point that divides a distribution in half: 50% of the data on the left of the median and the other 50% - on the right. To find the median, arrange the data in ascending (descending) order. If n is odd, the median is the observation with position If n is even, the median is the average of the middle two values with the positions n 1 2 + n n and 1 2 2 +
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7 25 Toyota MR2 21 23 Mersedes-Benz SLK230 20 22 Mazda Miata 19 22 Audi TT Roadster 18 20 Mersedes-Benz SLK320 17 20 Honda S 2000 16 20 BMW Z3 Roadster 15 20 Audi TT Quattro 14 19 Porsche Boxter
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Lec_2_Notes[1] stats 10 - DESCRIBING DISTRIBUTIONS...

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