1. Distributions, Percentiles, and Central Tendency
Monday, Sept. 30
Distributions, Percentiles,
and Central Tendency

5. The ogive gives you a good view of the relationship between scores and percentile rank.

6. Household Income by Language Group (Source: 1990 Census of Population and Housing)

7. A percentile rank of a score is a single number that gives the percent of cases in the specific reference group scoring at or below that score.

8. A percentile rank of a score is a single number that gives the percent of cases in the specific reference group scoring at or below that score.
PR = 100
(Ri - .5) n
Where Ri is the number of scores at or below that score.

9. In our sample of school districts, what is Tulare Elementary’s percentile rank for poor 2nd grade students?
Score = 576

10. CENTRAL TENDENCY
Mean
Median
Mode

11. The mode is the score with the highest frequency of occurrences.
It is the easiest score to spot in a distribution.
It is the only way to express the central tendency of a nominal
level variable.

12. The median.
The median is the middle-ranked score (50th percentile).
If there is an even number of scores, it is the arithmetic
average of the two middle scores.
The median is unchanged by outliers. Even if Bill Gates
were deleted from the U.S. economy, the median asset of
U.S. citizens would remain (more or less) the same.

13.  _ Xi X The Mean The mean is the arithmetic average of the scores.
_________ i X = N

14.  _ Xi X The Mean The mean is the arithmetic average of the scores.
The mean is the center of gravity of a distribution. Deleting
Bill Gates’ assets would change the national mean income. _  Xi
_________ i X = N

15. The mean of a group of scores is that point on the number line
such that the sum of the squared distances of all scores to that point
is smaller than the sum of the squared distances to any other point.

16. The Mean
The sum of squared deviations from the Mean is at the lowest value. _ ( ) 2  Xi - X
is lowest

17. The Mean
The sum of squared deviations from the Mean is at the lowest value. _ ( ) 2  Xi - X
is lowest _ X

18. The Mean
The mean is the arithmetic average of the scores.
The mean is the center of gravity of a distribution. Deleting
Bill Gates’ assets would change the national mean!
The sum of squared deviations from the Mean is at
the lowest value.
The mean is not a good measure of central tendency if there
are outliers.