1. Measures of Center and Absolute Mean Deviation Some old, some new……

2. Our objectives We will briefly review the measures of center and how to choose the appropriate measure of center for a set of data. We will calculate the absolute mean deviation of a set of values. An upcoming lesson will show why this measure, along with the interquartile range, may represent the spread of data.

3. Choosing the appropriate measure As you look at this data, do you see any outliers or a dominate mode? In this case, the mean is the best measure of center. What is it?

4. What about this set? Obviously there are no outliers. The mode is more than half of the data. The mode would be the measure of center we would choose to represent this data. These values have an obvious outlier, so the median is the most likely choice for measure of center. Let’s take a minute and study the effect the outlier has on the other values. They are ordered: 175 325 325 350 350 350 400 450The median is 350 with the outlier. Without the outlier, it would still be 350. The mode is not affected. It is 350 with or without the outlier. Actually, the mode could be a good measure, too. Let’s look at the effect of the outlier on the mean.

5. We found measures of variation for data sets: lower quartile, median, upper quartile, and interquartile range Let’s find these measures using the temperatures for 6 months for these two cities. The data is ordered. MeasuresAntelope, MTAugusta, ME Median Q 2 Q1Q1 Q3Q3 IQRange 50 47 30 32 70 66 40 34 Comparing the data, which city has a higher median temperature? Which city has a smaller interquartile range (spread)?

6. MeasuresAntelope, MTAugusta, ME Median Q 2 Q1Q1 Q3Q3 IQRange 50 47 30 32 70 66 40 34 20 30 40 50 60 70 80 Antelope, MT Augusta, ME

7. Now let’s look at a new way to measure the spread of data…..Absolute Mean Deviation. A line plot will help with the process of finding this measure. Plot the temperature values for Antelope, MT, on the first line. X X X Now find the mean temperature. The absolute mean deviation is the average of the difference in each value from the mean. 50 29 20 8 29 20 8

8. Now for the mean deviation of Augusta, ME. We will follow the same process. X X X X X X Find the mean temperature. Then find the differences in all values from the mean. The average of these differences in the absolute mean deviation. 49 21 17 8 26 17 4

9. For this set of data, we will just concentrate on the absolute mean deviation. It is easier to work with ordered data. Study the values and the range. Which set do you think will have a larger mean deviation? Why? 88 90 95 98 100 115 120 135 144 150

11. What have we done? Initially, we reviewed the way to choose the best measure of center. We reviewed measures of variation. We found the absolute mean deviation in very similar sets of data. We found the absolute mean deviation in data sets with a larger range and more variation in their measures.