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Methods: Measures of Central Tendency

Terms in this set (20)

Measures of Central Tendency
-Statistics used to represent the center of a distribution.
-Can describe a large data set, with a single, most typical or most representative value.
Mode
Most commonly occurring score.
Advantages:
-Score that actually occurred in the data set
-Unaffected by extreme scores
-Represents most common observation (some1 new mustang. Guess color! Red b/c most common)
Disadvantages:
-May not be representative of entire distribution of scores.
(1,2,3,4,5,11,11) mode: 11 (not representative)
Median
-Divides distribution in equal halves
-50% of scores fall above the median, 50% scores fall below median (Median= 50th percentile)

(N+1)/2 where N=# of scores
Median as discrete or continuous
Know if you're working with dis or cont data!
Discrete values: how many dogs, cats, etc? (2,3,4)
Contin values: test scores: 69.1,92.5,81.7
Median Rules
-Duplication of middle score, when even # of scores
MEDIAN AS FORMULA (SEE PP SLIDE)
Median Advantages
-Takes into account all the data in the distribution
-Unaffected by extreme scores (use when distributions are skewed)
-Use if have missing values in data set
-Open-ended distribution
(how many pets? _1 _2 _3+ (median gets rid of error in "3+"
-Use with an ordinal scale
Median Disadvantages
-Value may not exist in the data
-Does not enter readily into equations and more difficult to work with
-Treats all scores alike; differences in magnitude not taken into account
Mean
Amount each person gets when divide the total equally.
Focuses on distances.
Measuring distance from mean (above/below mean)
If you add the distances above the mean = distances below the mean (absolute value).
Sum of signed error from the mean will always=0
Mean Advantages
-Representative of every score in the distribution
-Closely related to variance and standard deviation
Mean Disadvantages
-Affected by extreme scores or outliers when you have only a limited number of scores in your distribution
-Value may not exist in the data (when mean is a decimal)
Weighted Mean
-Based on different sized groups using same DV
-To compare different sized sample sizes and make sure they weighed the same.
Characteristics of the Mean
Every score adds to total (sum of X) and contributes 1 point to the total sample size (n)
Changing a score in data set, changes sum of X, which produces a new Mean
-Exception: when adding a new score = exact value of mean (if new score = mean, it won't change)
Median & Mean in Graphs
Can be displayed in f histogram, f polygon, line plot, or bar graph.
Normal/Symmetric (No Skew)
Mean = Median = Mode
Positively Skewed
Mean > Median > Mode
(tail tapers to right)
Negatively Skewed
Mean < Median < Mode
(tail tapers to left)
L
(Median formula)
Lower Real Limit
-Lowest score in category containing the median minus .5
nL
(Median formula)
# of observations with scores less than L
nW
(Median formula)
# of observations within category containing the median
i
(Median formula)
Interval size
-Equal 1 for ungrouped frequency distribution
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