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Measures of Variation

Measures of Variation. Definition of Range. The range of a set of data is the difference between the greatest and least values of the set. Quartiles. Q 2 –the median. Line up the numbers in order and find the middle number.

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Measures of Variation

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  1. Measures of Variation

  2. Definition of Range • The range of a set of data is the difference between the greatest and least values of the set.

  3. Quartiles • Q2 –the median. Line up the numbers in order and find the middle number. • Q1 –is the lower quartile. It is the median of the bottom half of the set of data. • Q3 –is the upper quartile. It is the median of the upper half of the set of data. • Interquartile Range (IQR) – upper quartile minus the lower quartile. It represents the middle 50% of the set of data.

  4. Outliers • An outlier is a value that is much greater or much less than the rest of the set of data. • Acc. Only: It is any element of a set of data that is at least 1.5 interquartile ranges greater than the upper quartile or less than the lower quartile. • Outlier < Q1-1.5(IQR) or • Outlier > 1.5(IQR) + Q3

  5. Example • Find the range, median, upper quartile, lower quartile, and IQR of the set of data. • 11,16,17,19,24,25,30 • Range: 30 – 11=19 • Median: 19 • Upper quartile: 25 • Lower quartile: 16 • IQR: 9 • Acc. Only: Check for outliers: 1.5(9)=13.5. • 13.5 +25 = 38.5. No outliers up top. • 16 – 13.5 = 2.5. No outliers on bottom.

  6. Practice • Find the extremes, median, and the upper and lower quartiles of the data sets. • 5, 1, 5, 7, 2, 4, 1, 3, 5 • 5, 5, 6, 7, 8, 9, 0, 2, 10 • 5, 6, 8, 2, 5, 16, 23, 13, 23

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