1. Measure of Central Tendency
Vernon E. Reyes

2. A single number that repreresents the average
Useful way to describe a group
Central tendency – it is generally located towards the middle or center of the distribution where most of the data tend to be concentrated
Well-known measures of central tendency are: mode, the median, and the mean

3. Plot

4. Plot

5. Mode
The mode (Mo) is the only measure of central tendency used for NOMINAL DATA like religion, college major
It can also describe any level of measurement
The Mo is found through INSPECTION rather than COMPUTATION

6. Example 2 3 1 1 6 5 4 1 4 4 3 What id the Mo? = ____
What id the Mo? = ____
Note: the Mo is NOT the frequency
(f = 4)
(Mo = 1)

7. The mode can be unimodal or bimodal

8. Median
When ordinal or interval data are arranged in order or size, its possible to locate the median (Md or Mdn) – the middlemost point in a distribution
The position of the median value can be located by inspection or by formula
Position of the median = N+1 / 2

9. Odd or Even For odd number of cases (N) the median is easy to find
Using the formula (7+1) / 2 = 4
Therefore the fourth place is the median which is equal to 16

10. Odd or Even
For even number of cases (N) the median is always the point above or below where 50% of the cases will fall. !
Using the formula (8+1) / 2 = 4.5
Therefore the fourth place is the median which is equal to 16.5

11. Other note!
If the data are not in order from low to high (or high to low), you should put them in order first before trying to locate the median!

12. The MEAN The arithmetic mean X = mean (read as x bar X = raw score
N = Total number of score
Σ = sum (greek capital letter sigma)

13. Mo vs Md vs Mean “center of gravity”
A number that is computed which balances the scores above and below it
To understand the meaning of the MEAN we must look at the deviation
DEVIATION = X – X
Where X = any raw score
X = mean of the distribution

14. example +5 - 5 ------------------------------ X X – X
9 +3
6 0
5 -1
2 -4
X = 6
Notice that if we add all the deviations it will always equal to zero!
(+)5 + (-)5 = 0
Later we shall discuss standard deviation +5
- 5

15. Another example ------------------------------ X X – X1 2 3 5 6
X = ?
Find the mean!
Find the deviations!

16. The Weighted Mean The mean of means! Example:
Section 1: X 1 = N 1 = 28
Section 2: X 2 = 72 N 2 = 28
Section 3: X 3 = 79 N 2 = 28
= 236
3 3
= 78.97

17. Formula for weighted mean with unequal sizes
Xw = Σ Ngroup Xgroup
Ntotal
Xw = N1X1 + N2X2 +N3X3

18. The Weighted Mean The mean of means! Example: unequal N
Section 1: X 1 = N 1 = 95
Section 2: X 2 = 72 N 2 = 25
Section 3: X 3 = 79 N 2 = 18
95(85) + 25(72) + 18(79) =
11,297
138
= 81.86

19. Lets compare Mean, Median and Mode!X f
How old did you get married? 31 1 23 2 30 22 29 21 28 20 3 27 19 4 26 18 25
Find the mean median and mode 24