Central Tendency

Overview   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 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∑X∑ N μ = X∑X∑ n X =

THE 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∑X∑ n X =

Computing The Mean From A Frequency Distribution Table   Table 3–1 : statistics quiz scores for a section of π = 8 students. ƒX ƒ12401ƒ12401 QUIZ (X) SCORE

Characteristics 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,and1 The mean for this sample is = X∑X∑ n x 5 30 = 5 =6.00

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

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

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

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

CENTRAL TENDENCY AND THE SHAP OF THE DISTRIBUTION   Figure 3.16 measures of central tendency for three symmetrical distributions: normal, bimodal, and rectangular. mode mean median mode mean

CENTRAL TENDENCY AND THE SHAP OF THE DISTRIBUTION   Figure 3.17 measures of central tendency for skewed distributions. median mean mode mean median mode