1. Ibrahim Altubasi, PT, PhD The University of Jordan
Central Tendency
Ibrahim Altubasi, PT, PhD
The University of Jordan

2. Descriptive Statistics
Descriptive Statistics: statistical procedures used to
summarize, organize, and simplify data.
Shape of Distribution
Central Tendency
Variability
Mean, Median, Mode
A statistical measure that identifies a single
score (usually a central value) to serve as a
representative for the entire group.

3. Central Tendency Mean is the value obtained when the
sum of the scores is divided by the
number of scores:
Central Tendency
Mean (average)
Median
Mode

4. Central Tendency Properties related to mean:
• Change the value (including adding or
deleting a new observation score) in the
data may change the mean;
• Mean tends to be affected a lot by the
extreme observation(s);
• Add or subtract a constant from each
score in the data …;
• Multiplying or dividing each score by a
constant in the data…
Mean (average)
Median
Mode

5. Central Tendency Add or subtract a constant from each score in
the data …;
= 4.33
= ??
Amount of food (in grams) consumed before and after diet drug
injections (from Table 3.2, p.81 in G&W).

6. Central Tendency Multiplying or dividing each score by a
constant in the
data…
= 10
= ??
Measurement of five pieces of wood (Table 3.3, p.81 in G&W)

7. Central Tendency Averaging Means:
Suppose a teaching assistant gives his instructor the mean final exam scores for each of her two statistics classes. Suppose further that the instructor wishes to obtain a measure of the average performance of all her students, regardless of class. The mean final examination score was 77 in class 1 and 83 in class 2. What is the mean score of all her students in the two classes?
Case 1: n1 =20, n2 = 20
Case 2: n1 =10, n2 = 30

8. Central Tendency Unweighted mean is the average of two or more means.1 + 2
+ … + k
_________________
Unweighted = k
Weighted mean is the average of two or more means, calculated so that
each mean is weighted by the number of scores it represents .
ΣX1 + ΣX2 +…+ ΣXk
n n …+ nk k
__________________
_______________________
weighted =
n1+ n2+…+ nk
n1+ n2+…+ nk
Question: Can unweighted mean be equal to weighted mean? Under what
conditions?

9. Central Tendency
Central Tendency
The score that divides a distribution exactly in half-the 50th percentile
Mean (average)
Median
Mode
Ways to identify the median:
Order the raw score (from lowest to highest);
If n is an odd number, the median is the middle score.
If n is an even number, the median is the point halfway between the
middle two scores.

10. Central Tendency The score that has the greatest frequency.
Mean (average)
Median
Mode

11. Central Tendency
Measures of central tendency for three symmetrical distributions: normal,
bimodal, and rectangular

12. Central Tendency
Measures of central tendency for skewed distributions

13. Central Tendency Central tendency of variables on different scales of
measurement:
Interval or ratio: mean, median, mode
Ordinal: median, mode
Nominal: mode
With symmetric or nearly symmetric distributions, the
mean or median is preferred to the mode
The median is often used when the distribution is
asymmetric with a few extreme scores
Mode is the least stable measure of central tendency