Transcript of an observation. Interpret z-scores in context.

SWBAT: Use percentiles to locate individual values within distributions of data.
Interpret a cumulative relative frequency graph. Find the standardized value
(z-score) of an observation. Interpret z-scores in context.
Do Now: The test scores for 14 AP Statistics
students are given below. Find and interpret
the standard deviation for this data.
SWBAT: Use percentiles to locate individual values within distributions of data.
Interpret a cumulative relative frequency graph. Find the standardized value
(z-score) of an observation. Interpret z-scores in context.
Measuring Position: Percentiles
Definition:
The pth percentile of a distribution is the value with p percent of the
observations less than it.
Ex. Jenny earned a
score of 86 on her test.
How did she perform
relative to the rest of
the class?
SWBAT: Use percentiles to locate individual values within distributions of data.
Interpret a cumulative relative frequency graph. Find the standardized value
(z-score) of an observation. Interpret z-scores in context.
Cumulative Relative Frequency Graphs
Below is a frequency table that summarizes the ages of the first 44
U.S. presidents when they were inaugurated:
Age
40-44
45-49
50-54
55-59
60-64
65-69
Frequency
2
7
13
12
7
3
Relative
frequency
Cumulative
frequency
2/44 =
4.5%
2
7/44 =
15.9%
9
13/44 =
29.5%
22
12/44 =
27.3%
34
7/44 =
15.9%
41
3/44 =
6.8%
44
Cumulative
relative
frequency
2/44 =
4.5%
9/44 =
20.5%
22/44 =
50.0%
34/44 =
77.3%
41/44 =
93.2%
44/44 =
100%
Cumulative relative frequency (%)
Age of First 44 Presidents When They Were Inaugurated
100
80
60
40
20
0
40
45
50
55
60
65
Age at inauguration
70
SWBAT: Use percentiles to locate individual values within distributions of data.
Interpret a cumulative relative frequency graph. Find the standardized value
(z-score) of an observation. Interpret z-scores in context.
Cumulative relative frequency (%)
Interpreting Cumulative Relative Frequency Graphs
(a) Was Barack Obama, who was
inaugurated at age 47, unusually
young?
100
80
60
40
(b) Estimate and interpret the 65th
percentile of the distribution.
20
0
40
45
50
55
60
65
Age at inauguration
70
SWBAT: Use percentiles to locate individual values within distributions of data.
Interpret a cumulative relative frequency graph. Find the standardized value
(z-score) of an observation. Interpret z-scores in context.
Measuring Position: z-Scores
Definition: A z-score tells us how many standard deviations from the
mean an observation falls, and in what direction.
x  mean
z
standard deviation
Ex. Jenny earned a score of 86 on her test. The class mean is 80 and
the standard deviation is 6.07. What is her standardized score?
SWBAT: Use percentiles to locate individual values within distributions of data.
Interpret a cumulative relative frequency graph. Find the standardized value
(z-score) of an observation. Interpret z-scores in context.
Example: Jenny earned a score of 86 on her statistics test.
The class mean was 80 and the standard deviation was
6.07. She earned a score of 82 on her chemistry test. The
chemistry scores had a fairly symmetric distribution with a
mean 76 and standard deviation of 4. On which test did
Jenny perform better relative to the rest of her class?