1. Measures of Central Tendency
Chapter 3
Measures of Central Tendency
I Mode
A. Definition: the Score or Qualitative Category that Occurs With the Greatest Frequency
1. Mode (Mo) for the following data, number of required textbooks for Fred’s four classes, is 2.

2. _______________________________
Table 1. Taylor Manifest Anxiety Scores
_______________________________
(1) (2) f
_______________________________
74 1
73 1
72 0
71 2
Mo = 69
69 8
68 5
67 2
66 1
65 1
n = 28

3. II Mean
A. Definition: the Mean Is the Sum of Scores Divided by the Number of Scores
B. Formula

4. C. Summation Operator, (Greek capitol sigma)
D. Mean Formula for a Frequency Distribution
1. k = number of class intervals

5. _________________ f _________________ 74 1 74 n = 28 1,936
Table 2. Taylor Manifest
Anxiety Scores
_________________
(1) (2) (3) f
_________________
72 0 0
n = 28 1,936

6. 1. If n is odd and the scores are ordered, the median
III Median (Mdn)
A. Definition: the Median Divides Data Into Two Groups Having Equal Frequency
1. If n is odd and the scores are ordered, the median
is the (n + 1)/2th score from either end of the number line.
2. If n is even, the median is the midway point
between the n/2th score and the n/2 + 1th
score from either end of the number line.

7. B. Computational Examples
1. Determination of Mdn when n is odd
2. Determination of Mdn when n is even

8. 3. Determination of Mdn when n is even (a) or odd
3. Determination of Mdn when n is even (a) or odd (b), and the frequency of the middle score value is greater than 1

9. 4. Determination of Mdn when n is even and the
4. Determination of Mdn when n is even and the frequency of the middle score value is greater than 1

10. C. Computation of Mdn for a Frequency Distribution
1. Formula when scores are cumulated from below
Xll = real lower limit of the class interval
containing the median
i = class interval size
n = number of scores
fb = number of scores below Xll
fi = number of scores in the class interval containing the median

11. 2. Formula for the Mdn when scores are cumulated
from above
Xul = real upper limit of class interval
containing the median
fa = number of scores above Xul

12. __________________________
Table 3. Taylor Manifest Anxiety
Scores
_____________________________
__________________________
68 5 9
67 2 4
66 1 2
65 1 1
n = 28

13. IV Relative Merits of the Mean, Median, and Mode
V Location of the Mean, Median, and Mode
in a Distribution

14. A. Weighted Mean VII Summation Rules A. Sum of a Constant (c)
VI Mean of Two or More Means
A. Weighted Mean
VII Summation Rules
A. Sum of a Constant (c)

15. B. Sum of a Variable (Vi)
C. Sum of the Product of a Constant and a Variable
D. Distribution of Summation