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Measures of Variation

Measures of Variation. TOC #6. Vocabulary. Lower Quartile – the median of the lower half of data. Upper Quartile – the median of the upper half of data. Interquartile Range – the difference between the upper quartile and lower quartile. Vocabulary. Quartile – Represents 25% of the data

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Measures of Variation

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  1. Measures of Variation TOC #6

  2. Vocabulary • Lower Quartile – the median of the lower half of data. • Upper Quartile – the median of the upper half of data. • Interquartile Range – the difference between the upper quartile and lower quartile.

  3. Vocabulary • Quartile – Represents 25% of the data • 4 quartiles = 100%

  4. Example 1 • Find the measures of variation of the following data: • 67 75 81 67 75 85 69 Step 1: Order the data from least to greatest. • 67 69 73 75 75 81 85

  5. Example 1 continued Step 2: Find the median: • 67 69 73 + 75 75 81 85 2 Median = 74

  6. Example 1 continued • Step 3: The median divides the data in half: • 67 69 73 75 75 81 85 lower upper quartile quartile

  7. Example 1 continued • Lower quartile: (median of lower half) 67 + 69= 68 2 • Upper quartile: (median of upper half) 75 + 81= 78 2

  8. Example 1 continued • Find the interquartile range: Upper quartile – Lower quartile 78 – 68 = 10

  9. Example 2 • Find the quartiles and interquartile range for the given data: 42, 22, 31, 27, 24, 38, 35

  10. First put it in order… • 22, 24, 27, 31, 35, 38, 42 Next, find the median… • 22, 24, 27, 31, 35, 38, 42 Now identify the lower half of data: 22, 24, 27 The lower quartile is the median of the lower half which is 24.

  11. Now identify the upper half of data: 35, 38, 42 • The upper quartile is the median of the upper half of data which is 38. • The interquartile range is the difference between the quartiles: 38 – 24 = 14

  12. Example 2 recap • So… • The median is  31 • The upper quartile is  38 • The lower quartile is  24 • The interquartile range is  14

  13. Example 3 • Find the quartiles and interquartile range for the given data in this stem and leaf plot: 2 | 4 7 9 3 | 0 6 7 4 | 5 | 0 1 1

  14. First put it in order… • 24, 27, 29, 30, 36, 37, 50, 51, 51 Next, find the median… • 24, 27, 29, 30, 36, 37, 50, 51, 51 Now identify the lower half of data: 24, 27, 29, 30 The lower quartile is the median of the lower half which is 27 + 29 = 56 2 2 The LOWER QUARTILE = 28

  15. Now identify the upper half of data: 37, 50, 51, 51 • The upper quartile is the median of the upper half of data which is ½ way between 50 and 51 = 50.5. • The interquartile range is the difference between the quartiles: 50.5 – 28 = 22.5

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