210-Class-Handout-Oct-01

50 professor savage 3 statistics 210 measures of

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Unformatted text preview: avage 3 Statistics 210 MEASURES OF DISPERSION (i) Range - difference between maximum and minimum Ungrouped Data: maximum: 5, minimum: 0 Range: 5 Grouped data: maximum: $99,999.49, minimum: -$0.49 Range: $100,000 (ii) Semi-Interquartile Range – half the distance between the 25th percentile and 75th percentile Q1 = 0.75 (2.75 value) Q3 = 3.25 (8.25 value) Semi-interquartile range = (Q3 - Q1)/2 = 1.25 Grouped Data Q1 = (2.75th value) $19,999.50 + 1.75/5 ($20,000) = $26,999.50 Q3 = (8.25 value) $59,999.50 + 0.25/1 ($20,000) = $64,999.50 Semi-interquartile range = (Q3 - Q1)/2 = $19,000 (iii)Variance For data on a population: ∑ For data from a sample: ∑ Our data are samples. So for ungrouped data (mean was 2.1): . . Alternatively: . . . . . 2.54 ∑ 1 . . . . Professor Savage 4 Statistics 210 . . 2.54 For Grouped Data (mean = $41,999.50) ∑ Class Freq 0- $19,999.49 $19,999.50 - $39,999.49 $39,999.50 - $59,999.49 $59,999.50 - $79,999.49 $79,999.50 - $99,999.49 1 5 2 1 1 Midpoint 1 Midpoint (midpo...
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