1. Summary Statistics and Mean Absolute Deviation MM1D3a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions. b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters. MM1D4. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

2. Vocab: Measures of Central Tendency Mean: aka: average; denoted by the symbol x, which is read x-bar. Median: the middle number when values are written in numerical order. Mode: the value that occurs most frequently Measure of dispersion: describes the spread of data Range: the difference between the greatest value and least value of a numerical set of numbers Deviation from the mean: the difference of a data value and the mean of a data set Mean absolute deviation: the average deviation of the data from the mean.

3. Mean absolute deviation: the average deviation of the data from the mean. The mean absolute deviation of the data x 1, x 2, ……. x n is given by: So, to find the mean absolute deviation, you first have to find the ________!!

4. Example 1

5. Example 2

6. Example 3 Use the data:

7. Example 4

8. Example 5

9. Homework Pg 365: 2 – 16 even Write problems and show work for credit!

10. Sample Statistics Median: Separates the data into ___ equal parts Quartiles: Separate the data into ____ equal parts Upper Quartile: The median of the upper half of the data Lower Quartile: The median of the lower half of the data Range: The difference between the highest and lowest values in a data set Interquartile Range: The difference between the upper quartile and the lower quartile.

11. Read this Plot! List the Following: Median: Range: Quartile 1: Quartile 2: Quartile 3: Interquartile Range:

12. Example 1

13. Compare Mean Median Range Upper Quartile Lower Quartile IQR

14. Example 2

15. Example 3