Section 1.1
Part 4
AP Statistics
September 8, 2008
CASA
Using Percents

It is sometimes difficult to compare the
“straight” numbers. For example:
 Ty
Cobb in his 24 year baseball career had
4,189 hits. Pete Rose also played for 24 years
but he collected 4,256 hits. Was Pete Rose a
better batter than Ty Cobb?
AP Statistics, Section 1.1, Part 4
2
Using Percents
Ty Cobb had a career batting average of
.366. (He got a hit 36.6% of the time)
 Pete Rose had a career batting average of
.303.
 Comparing the percentage, we get a
clearer picture.

AP Statistics, Section 1.1, Part 4
3
Relative Frequency
When constructing a histogram we can
use the “relative frequency” (given in
percent) instead of “count” or “frequency”
 Using relative frequency allows us to do
better comparisons.
 Histograms using relative frequency have
the same shape as those using count.

AP Statistics, Section 1.1, Part 4
4
Finding Relative Frequency
For each count in a class, divide by the
total number of data points in the data set.
 Convert to a percentage.

AP Statistics, Section 1.1, Part 4
5
Finding Relative Frequency
Class
Frequency
40-44
2
45-49
6
50-54
13
55-59
12
60-64
7
65-69
3
Total
43
AP Statistics, Section 1.1, Part 4
6
Finding Relative Frequency
Class
Frequency
Relative
Frequency
40-44
2
2/43=4.7%
45-49
6
6/43=14.0%
50-54
13
13/43=30.2%
55-59
12
12/43=27.9%
60-64
7
7/43=16.3%
65-69
3
3/43=7.0%
Total
43
AP Statistics, Section 1.1, Part 4
7
Histograms
AP Statistics, Section 1.1, Part 4
8
Finding Cumulative Frequency
Class
Frequency
Relative
Frequency
Cumulative
Frequency
40-44
2
2/43=4.7%
2
45-49
6
6/43=14.0%
8
50-54
13
13/43=30.2%
21
55-59
12
12/43=27.9%
33
60-64
7
7/43=16.3%
40
65-69
3
3/43=7.0%
43
Total
43
AP Statistics, Section 1.1, Part 4
9
Finding
Relative Cumulative Frequency
Class
Frequency
Relative
Frequency
Cumulative
Frequency
Relative
Cumulative
Frequency
40-44
2
2/43=4.7%
2
2/43=4.7%
45-49
6
6/43=14.0%
8
8/43=18.6%
50-54
13
13/43=30.2%
21
21/43=48.8%
55-59
12
12/43=27.9%
33
33/43=76.7%
60-64
7
7/43=16.3%
40
40/43=93.0%
65-69
3
3/43=7.0%
43
43/43=100%
Total
43
AP Statistics, Section 1.1, Part 4
10
Percentiles
“The pth percentile of a distribution is the
value such that p percent of the
observations fall at or below it.”
 If you scored in the 80th percentile on the
SAT, then 80% of all test takers are at or
below your score.

AP Statistics, Section 1.1, Part 4
11
Percentiles
Class
Relative
Cumulative
Frequency
40-44
2/43=4.7%
45-49
8/43=18.6%
50-54
21/43=48.8%
55-59
33/43=76.7%
60-64
40/43=93.0%
65-69
43/43=100%



It is easy to see the
percentiles at the
breaks.
“A 64 year old would
be at the 93rd
percentile.”
What do you do for a
57 year old?
Total
AP Statistics, Section 1.1, Part 4
12
Ogives (o-JIVE) or
“Relative Cumulative Frequency Graph”
Class
Relative
Cumulative
Frequency
40-44
2/43=4.7%
45-49
8/43=18.6%
50-54
21/43=48.8%
55-59
33/43=76.7%
60-64
40/43=93.0%
65-69
43/43=100%
Total
AP Statistics, Section 1.1, Part 4
13
Time Plots
Time (measured in seconds, days,
months, years, etc.) is always on the xaxis.
 Use time plots to see trends related to
time like…

 Seasonal
variation
 Growth trends
AP Statistics, Section 1.1, Part 4
14
Assignment

Exercises 1.19 – 1.29 odd, The Practice of
Statistics.
AP Statistics, Section 1.1, Part 4
15