PSYC 2300 Lecture Notes - Lecture 10: Central Tendency, Frequency Distribution
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Central Tendency
1. Overview of central tendency
a. Central tendency: statistical measure to define center of a distribution
b. Purpose: find single-most typical or representative score of entire group
c. Mean—3 definitions
i. Sum of scores divided by # of scores in data
ii. Average amount
iii. Balancing point of distribution
2. Mean
a. Computed in the same manner because it’s the sum of all scores divided by the #
of scores in the data
b. Population:
c. Sample:
d. Weighted mean
i. 2 or more groups with unequal sample sizes
ii. 3 ways to compute—use of method depends on available data
1. If you have all raw data, obtain average student grade by
averaging all grades without regard to classes
2. If only group means and # of individuals in each group are
available, weight class means by # students in a class
3. If you have 2 sets of sums and sample sizes, combine information
iii. Which one do you use?
1. Raw data given—method 1
2. Group sample sizes and means given—method 2
3. Sum of x’s and sample sizes given—method 3
e. Characteristics of mean
i. Changing value of a score changes the mean
ii. Introducing a new score (or removing a score) usually changes the mean
unless score added or removed is exactly equal to the mean
iii. Adding or subtracting a constant from each score changes the mean by
the same constant
iv. Multiplying or dividing each score by a constant multiplies or divides the
mean by that constant
3. Median
a. Median: midpoint of scores in a distribution
b. Listed in order from smallest to largest divides scores into 2 groups of equal sizes
c. Also called 50th percentile
d. Because it ignores most of the data, uninfluenced by extreme scores
e. Cannot be manipulated algebraically
f. Locating median—odd # of scores