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)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000
Household Income
Percentage
Hmong
Cambodian
Lao
Spanish
Samoan
Armenian
Tongan
Indonesian
Vietnamese
Rumanian
Portuguese
Russian
Arabic
Korean
Persian
Ukrainian
Chinese
Punjabi
Japanese
Pilipino
Ilocano
Hindi
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.
9.
10.
11. The mode.
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. The Mean
The mean is the arithmetic average of the scores.
X
_
=
i
Xi
_________
N
14. 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.
X
_
=
i
Xi
_________
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.
X
_
Xi -
( )
2
is lowest
17. The Mean
The sum of squared deviations from the Mean is at the lowest value.
X
_
Xi -
( )
2
is lowest
1.6
1.4
1.2
1.0
.8
.6
.4
DIS2
610
600
590
580
570
560
550
540
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.
