Measures of Central Tendency

1. Measures of Central Tendency Where is the “center” of a distribution?

2. Three Measures of Central Tendency * Note that when distributions are symmetrical, the mean, the median and the mode will all be the same value.

3. The Mean (or Average) 11 is the number of sample values

4. The Deviations away from the sample mean of each sample value will always add to 1. The mean = 2. So 3 – 2 = a deviation of 1, 8 - 2 = a deviation of 6, and so on. DATA value – Mean Value = DEVIATION value

5. The Deviations can be displayed graphically as in Figures 2-2 and 2-3.

6. When data is expressed in a Frequency Table (instead of listed individually), the mean can be calculated as:

7. The Median There are 5 values lower than 2 There are 5 values higher than 2

8. The Median can be depicted graphically, as in Figures 2-4 and 2-5.

9. The Median can be depicted on a Table, as in Table 2-2.

10. When there are an even number of sample observations, there is no one median observations. To get the median value, get the average value of the two middle values surrounding the median. Median The Median

11. The Mode

13. The Mode is 3, with the highest frequency Because there is one mode only, this distribution is “unimodal”.

14. This distribution is “bimodal”, with modes at both 3 and 6.

15. Distribution Shapes