1. Mean and Median

2. One descriptive term for a set of data is the measure of central tendency. Most books list three things when talking about measures of central tendency: 1. Mean or average 2. Median 3. Mode

3. Mean or average is probably a very common term for all of you. To find the mean for a set of data, simply add all your observations and divide by the number of observations you have. A basketball player scores 10, 9, 11, 8, and 4 points in the past 5 games. What is the mean number of points he has scored over the past 5 games? Find the total number of points scored 10 + 9 + 11 + 8 + 4 = 42 5 games played Mean is 42/5 = 8.4 points per game

4. What is the affect of an outlier (extreme value) on our mean? A basketball player scores 10, 9, 11, 8, and 4 points in the past 5 games. In his next game he scores 28 points. What happens to the mean? Find the total number of points scored 10 + 9 + 11 + 8 + 4 + 28 = 70 6 games played Mean is 70/6 = 11. 7 points per game (rounded to nearest tenth) An outlier will pull the mean towards it greatly. Our mean changed by over 3 points with the outlier. Therefore, if our data contains an extreme value, the mean may not be a good measure to describe the center of our data.

5. Median is the middle value of a set of data. There are two situations to look at. Odd number of observations: Our median will be one of our observations. We list our data in order, cross off max and min values, continue crossing max and mins off of remaining data until 1 value remains. Data: 10, 13, 15, 18, 21 Cut off min and max: 13, 15, 18 Cut again: 15 (median) Even number of observations: We use the same process, but there will be two observations remaining. We find the mean of these two values. Therefore, our median may or may not be one of the values in our data set. Data: 10, 15, 18, 24, 30, 38 Cut off max and min: 15, 18, 24, 30 Cut again: 18, 24 Find the mean: 21 is our median

6. A basketball player scores 10, 9, 11, 8, and 4 points in the past 5 games. What is the median number of points he has scored over the past 5 games? Put data in order: 4, 8, 9, 10, 11 Cut off max and min: 8, 9, 10 Cut again: 9 Median = 9

7. What is the affect of an outlier (extreme value) on our median? A basketball player scores 10, 9, 11, 8, and 4 points in the past 5 games. In his next game he scores 28 points. What happens to the median? Put data in order: 4, 8, 9, 10, 11, 28 Cut off max and min: 8, 9, 10, 11 Cut again: 9, 10 Median = 9.5 An outlier will pull the median towards it, but not by a large amount. Our median only changed by 0.5 points with the outlier. Therefore, if our data contains an extreme value, the median is actually a good measure to describe the center of our data set.

8. The mode of a data set is the most common value. It is often discussed at the same time as mean and median, but is not always a measure of center. Some sets may not have a mode: 1, 2, 3, 4, 5: no observations happen more than the others. Some sets may have a single mode: 1, 1, 2, 3, 4, 5: the mode is 1 since it occurs more than the other values. Some may have more than one mode: 1, 1, 2, 2, 3, 4, 5, 6: 1 and 2 both occur twice and is more than the other observations, so our modes are 1 and 2. In general, if there are 3 or more that happen the same number of times and more than the rest, I consider there to be no mode.