1. Section 6.8 Compare Statistics from Samples

2. Vocabulary Quartile: The median of an ordered data set Upper Quartile: The median of the upper half of an ordered data set Lower Quartile: The median of the lower half of an ordered data set Interquartile Range: The difference between the upper quartile and the lower quartile of a data set

3. Example 1 C ompare statistics from different samples The data sets below give the number of computers assembled by each employee during one month in the East production division and the West production division. Compare the data using the mean, median, range, and interquartile range. EAST: 19, 18, 17, 16, 15, 13, 12, 10 WEST: 21, 20, 19, 18, 17, 16, 14, 9

4. EAST x = 19 + 18 + 17 + 16 + 15 + 13 + 12 + 10 =15 8 Median: 16 + 15 = 15.5 2 Range: 19 - 10 = 9 Lower Quartile: 13 + 12 = 12.5 2 Upper Quartile: 18 + 17 = 17.5 2 Interquartile Range: 17.5 - 12.5 = 5

5. WEST x = 21 + 20 + 19 + 18 + 17 + 16 + 14 + 9 8 Median: 18 + 17 = 17.5 2 Range: 21 - 9 = 12 Lower Quartile: 16 + 14 = 15 2 Upper Quartile: 20 + 19 = 19.5 2 Interquartile Range: 19.5 - 15 = 4.5

6. The West's mean is greater than the East's mean, so the West averaged more computers assembled per person. The East's range is less than the West's, so their data is less spread out. The West's interquartile range is less than the East's so the West's middle 50% of the data shows less variation than the middle 50% of the East's data.

7. checkpoint #1

8. Example 2 C ompare sample and population statistics At the end of the month, summary production statistics are calculated for the entire company. The table below shows the summary data for the North and South divisions. Find the averages of the summary statistics from the four samples: the East and West divisions from Ex. 1, the North division and the South division. MeanMedianRang e IQR N17.515.573 S13.312116 A14.913105.5

9. Average mean: x = 15 + 16.75 + 17.5 + 13.3 = 15.6375 4 Average median: 15.5 + 17.5 + 15.5 + 12 = 15.125 4 Average range: 9 + 12 + 7 + 11 = 9.75 4 Average Interquartile Range: 5 + 5.4 + 3 + 6 = 4.625 4

10. The average mean and median are more than the corresponding population measures. The average range and interquartile range are less than the corresponding population measures.

11. checkpoint #2

12. Essential Question How do you compare statistics from samples?