Measures of Central Tendency Flashcards
What are measures of central tendency?
They represent the most typical, central, or common score in a distribution.
Key measures:
Mode
Median
Mean
What is the mode?
The category or score that appears most frequently in a distribution.
When is the mode used?
The only measure appropriate for nominal variables.
Can also be used for ordinal and interval-ratio variables.
What are limitations of the mode?
Some distributions have no mode.
Some have multiple modes.
What is the median?
The score that divides a distribution into two equal halves, with 50% of cases above and 50% below.
How do you find the median?
Arrange scores from highest to lowest.
If n is odd, the median is at position (n+1)/2
If n is even, the median is the average of the two middle scores.
When is the median used?
For ordinal and interval-ratio variables (not nominal).
What is the mean?
The arithmetic average of all scores in a dataset.
Why is the mean commonly used?
It incorporates all values in the dataset.
What are three key characteristics of the mean?
Balance point: The sum of differences from the mean always equals zero.
Minimized variation: The mean is the point where variation is smallest.
Affected by every score, including outliers (extreme values).
How do outliers affect the mean?
Outliers pull the mean in their direction, making it less representative of the typical value.
What happens in a symmetrical distribution?
Mode = Median = Mean (Bell Curve)
What happens in a positively skewed distribution?
Mode < Median < Mean
Tail extends to the right (higher values).
What happens in a negatively skewed distribution?
Mode > Median > Mean
Tail extends to the left (lower values).
When should the mean NOT be used?
When the data is skewed, since extreme values distort the average.
