Central TendencyCentral Tendency

OverviewOverview Central tendency is a statistical

measure that identifies a single score as representative on an entire distribution. The goal of central tendency is to find the single score that is most typical or most reprehensive of the entire group.

THE MEANTHE MEAN

The mean for a distribution is the sum of the scores divided by the number of scores.

The formula for population is :-

Sample mean =

X∑

Nμ =

X∑

nX =

THE WEIGHED MEANTHE WEIGHED MEAN often in necessary to combine two

sets of scores and then find the overall mean for the combined group.

The solution to this problem is straightforward if you remember the definition of the mean :

X∑

nX =

Computing The Mean From A Computing The Mean From A Frequency Distribution TableFrequency Distribution Table

Table 3–1 : statistics quiz scores for a section of π = 8 students.

QUIZ (X) SCORE

109876

ƒ

12401

ƒX

10183206

Characteristics Of The MeanCharacteristics Of The Mean

1- Changing a score or introducing a new score changing the value of any score will change the mean. For example , the quiz scores for psychology lab section consist of

9, 8, 7, 5, and 1 The mean for this sample is

=X∑

nx

55

30=

5= 6.00

Characteristics Of The MeanCharacteristics Of The Mean

2- Adding or subtracting a constant from each score.

Table 3.2 amount of food (in grams) consumed during baseline session.

RAT'S IDENTIFICATION AMOUNT (X) A 6 B 3 ∑X= 26

C 5

D 3 n=6 E 4

F 5 X=4.33

Characteristics Of The MeanCharacteristics Of The Mean

3- Multiplying or dividing score by a constant If every score in a distribution is multiplied by a constant value, the mean will be changed in the same way.

THE MEDIANTHE MEDIAN

The median is the score that divides a distribution exactly in half.

13579

MEDIANMEDIAN

THE MODETHE MODE

The mode is the score or category that has the greatest frequency .

THE MODETHE MODE

Figure 3.9Figure 3.9 the relationship between the relationship between time of day and number of fish time of day and number of fish caught.caught.

12345678910111213141516012345678910

Frequency

Noon Tim of day

THE MODETHE MODE

Figure 3.10 major field of study for n= 9 students enrolled in an experimental psychology laboratory section.

Business

Sociology Psychology Biology

0

1

2

3

4

5

6

CENTRAL TENDENCY AND THE SHAP OF THE DISTRIBUTION

Figure 3.16 measures of central tendency for three symmetrical distributions: normal, bimodal, and rectangular.

Symetrical Distribution

mode modemeanmedian

Symmetrical distributuon

medianmode

mean

CENTRAL TENDENCY AND THE SHAP OF THE DISTRIBUTION

Figure 3.17 measures of central tendency for skewed distributions.

Skewed distribution

Negative Skew

Skewed distribution

Positive skew

medianmea

nmod

e

meanmedia

nmode