2-3_describ_distr_numerically

2-3_describ_distr_numerically - 2.3 Describing...

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2.3 Describing Distributions Numerically Numerical and More Graphical Methods to Describe Univariate Data
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2 characteristics of a data set to measure center measures where the “middle” of the data is located variability measures how “spread out” the data is
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The median: a measure of center Given a set of n measurements arranged in order of magnitude, Median= middle value n odd mean of 2 middle values, n even Ex. 2, 4, 6, 8, 10; n =5; median=6 Ex. 2, 4, 6, 8; n =4; median=(4+6)/2=5
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Student Pulse Rates (n=62) 38, 59, 60, 60, 62, 62, 63, 63, 64, 64, 65, 67, 68, 70, 70, 70, 70, 70, 70, 70, 71, 71, 72, 72, 73, 74, 74, 75, 75, 75, 75, 76, 77, 77, 77, 77, 78, 78, 79, 79, 80, 80, 80, 84, 84, 85, 85, 87, 90, 90, 91, 92, 93, 94, 94, 95, 96, 96, 96, 98, 98, 103 Median = (75+76)/2 = 75.5
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Medians are used often Year 2011 baseball salaries Median $1,450,000 (max=$32,000,000 Alex Rodriguez; min=$414,000) Median fan age : MLB 45 ; NFL 43 ; NBA 41 ; NHL 39 Median existing home sales price : May 2011 $166,500 ; May 2010 $174,600 Median household income (2008 dollars) 2009 $50,221 ; 2008 $52,029
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The median splits the histogram into 2 halves of equal area
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Examples Example: n = 7 17.5 2.8 3.2 13.9 14.1 25.3 45.8 Example n = 7 (ordered): 2.8 3.2 13.9 14.1 17.5 25.3 45.8 Example: n = 8 17.5 2.8 3.2 13.9 14.1 25.3 35.7 45.8 Example n =8 (ordered) 2.8 3.2 13.9 14.1 17.5 25.3 35.7 45.8 m = 14.1 m = (14.1+17.5)/2 = 15.8
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Below are the annual tuition charges at 7 public universities. What is the median tuition? 4429 4960 4960 4971 5245 5546 7586 1. 5245 2. 4965.5 3. 4960 4. 4971
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Below are the annual tuition charges at 7 public universities. What is the median tuition? 4429 4960 5245 5546 4971 5587 7586 1. 5245 2. 4965.5 3. 5546 4. 4971
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Measures of Spread The range and interquartile range
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Ways to measure variability range=largest-smallest OK sometimes; in general, too crude; sensitive to one large or small data value The range measures spread by examining the ends of the data A better way to measure spread is to examine the middle portion of the data
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m = median = 3.4 Q 1 = first quartile = 2.3 Q 3 = third quartile = 4.2 1 1 0.6 2 2 1.2 3 3 1.6 4 4 1.9 5 5 1.5 6 6 2.1 7 7 2.3 8 6 2.3 9 5 2.5
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2-3_describ_distr_numerically - 2.3 Describing...

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