Chapter 4: Measures of Central Tendency Flashcards
1
Q
Measures of Central Tendency
A
Numerical values which give us an idea as to where the center of a distribution is
-Can be represented by several statistics: mean, median & mode
2
Q
The Mode
A
Most common score- obtained from the largest value of objects
Advantages
- Always a score w/in the data
- Represents the largest # of people w the same score
- Applicable to nominal, ordinal & interval/ ratio (all scales)
- Not heavily influenced by outliers
- Easy to calculate
Disadvantages
- May not represent the entire collection of numbers; doesn’t take the spread of scores into account
- If differences in frequency are small, a change in one score could change the mode dramatically
- Ambiguous: if there is more than one mode, which mode can be considered to be the typical value?
3
Q
The Median
A
Middle score in an ordered data set
- Corresponds to the point having 50% of observations below/ above it when arranged in a numerical order
- Located at [ ( N + 1 ) / 2 ]
Advantages
- Unaffected by extreme scores/ outliers
- Calculation doesn’t require assumptions about interval properties of the scale
Disadvantages
- Doesn’t readily enter into eq’ns & is more difficult to work with
- Not as stable from sample to sample
- Can not be used with nominal data
- Value may not actually exist in the data
- Does not take the spread of scores into accout
4
Q
The Mean (Average)
A
- Sum of scores divided by the number of scores
- Most common used measure of central tendency
- -Weighted means exist (ie. GPA calculations)
- Sum of the deviation scores around the mean is zero
- Sum of the squared deviation scores around the mean is a minimum (relative to deviations around any other point)
Advantages
- Most common score in the public (most applicable)
- Can use the mean in an eq’n & manipulate it through the normal rules of algebra
- -Can write an eq’n that defines the mean
- -Is used in statistical eq’ns
- Is a stable, better estimate of the population
- Every data point contributes to it
- More reliable than many other measures (ie. median)
Disadvantages
- Influenced by extreme scores- its value may not exist in the data
- -Interpretation in terms of underlying variable requires some faith in interval properties of the data
- -Sensitive to outliers
- Requires an interval/ ratio scale
- Value may not exist in the data
- -Ie. average family = 3.1 people… but what’s 0.1 of a person?
5
Q
Trimmed Means
A
Mean resulting from trimming/ discarding a fixed % of the extreme observations
-Eliminates possible outliers, common in treating skewed data
