Central Tendency
A. Measures of Central Tendency
A measure of central tendency is a statistic that indicates the middle, center or average of a distribution;
provides a single score to represent the entire group of scores.
1. Mean:
Arithmetic average; takes into account the value of each and every score in the distribution;
considered the balance point, or fulcrum, of the distribution
M =
N
X
∑
Examples
1) Data set: 2, 3, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9
2) Data set: 2, 3, 4, 5, 5, 5, 6, 6, 6, 7, 20, 21
2. Median:
Score that divides the distribution in half such that half of the scores are greater and half of the
scores are less than the median (Mdn)
Median location =
2
1
+
N
=
th
score
Put scores in order and count from one end to median location. The score at that location is the median.
Examples: 1)
Data set: 2, 3, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9
2)
Data set: 2, 3, 4, 5, 5, 5, 6, 6, 6, 7, 20, 21
3) Frequency distribution:
X
f
7
4
6
9
5
24
4
19
3
10
2
7
1
6
3. Mode:
The most frequently occurring score in the distribution