1. Chapter 2
D E S C R I P T I V E S TA T I S T I C S
SECTIONS 6-9

2. 2.6 Percentiles
 Quartiles are specific examples of percentiles. The first
quartile is the same as the 25th percentile and the third
quartile is the same as the 75th percentile.
 The nth percentile represents the value that is greater than or
equal to n% of the data.

3.  Jennifer just received the results
EXAMPLE of her SAT exams. Her SAT
Composite of 1710 is at the 73rd
Consider each of
the following
percentile. What does this mean?
statements about
percentiles.
 Suppose you received the highest
score on an exam. Your friend
scored the second-highest
score, yet you both were in the
99th percentile. How can this be?

4. Number
Frequency RF CRF
EXAMPLE of Tickets
0 6 0.08 0.08
The following data 1 18 0.24 0.32
set shows the
number of parking 2 12 0.16 0.48
tickets received.
3 11 0.15 0.63
4 9 0.12 0.75
5 6 0.08 0.83
6 5 0.07 0.90
7 4 0.05 0.95
8 2 0.03 0.98
9 1 0.01 0.99
10 1 0.01 1

5.  Find and interpret the 90th
EXAMPLE percentile.
The following data
set shows the  Find and interpret the 20th
number of parking
tickets received.
percentile.
 Find the first quartile, the
median, and the third quartile.
 Construct a box plot.

6. 2.6 IQR and outliers


7. Number
Frequency RF CRF
EXAMPLE of Tickets
0 6 0.08 0.08
The following data 1 18 0.24 0.32
set shows the
number of parking 2 12 0.16 0.48
tickets received.
3 11 0.15 0.63
4 9 0.12 0.75
5 6 0.08 0.83
6 5 0.07 0.90
7 4 0.05 0.95
8 2 0.03 0.98
9 1 0.01 0.99
10 1 0.01 1

8. EXAMPLE  Find the inner quartile range of
the data set.
The following data
set shows the
number of parking
tickets received.  Do any of the data values appear
to be outliers

9. 2.7 Measures of Center


10. EXAMPLE
Find the mean 1. 4.5, 10, 1, 1, 9, 14, 4, 8.5, 6, 1, 9
median and mode of
the following data
set.
Use technology to
find statistical
information.

11. Number
Frequency RF CRF
EXAMPLE of Tickets
0 6 0.08 0.08
The following data 1 18 0.24 0.32
set shows the
number of parking 2 12 0.16 0.48
tickets received.
3 11 0.15 0.63
Find the mean, 4 9 0.12 0.75
median, and mode.
5 6 0.08 0.83
Use technology to 6 5 0.07 0.90
find statistical
information. 7 4 0.05 0.95
8 2 0.03 0.98
9 1 0.01 0.99
10 1 0.01 1

12. 2.9 Measures of Spread
 The final statistics we would like to be able to find are
measures that tell us how spread out the data is about the
mean.
 The two statistics that are most commonly used to measure
spread are standard deviation and variation.
 Standard deviation gives us another way to identify possible
outliers: a data value might be an outlier if it is more than
two standard deviations from the mean.

13. 2.9 Calculating Standard Deviation and Variance

14. EXAMPLE
Find the standard 1. 4.5, 10, 1, 1, 9, 17, 4, 8.5, 5, 1, 9
deviation and
variance of the data
set assuming that it
is a sample.
Use standard
deviation to
determine if any
values are possible
outliers.
Use technology to
find statistical
values.

15. Number
Frequency RF CRF
EXAMPLE of Tickets
0 6 0.08 0.08
The following data 1 18 0.24 0.32
set shows the
number of parking 2 12 0.16 0.48
tickets received.
3 11 0.15 0.63
Find the standard
deviation and 4 9 0.12 0.75
variance of the data 5 6 0.08 0.83
set assuming that it
is a sample. 6 5 0.07 0.90
Use standard 7 4 0.05 0.95
deviation to
determine if any
8 2 0.03 0.98
values are possible 9 1 0.01 0.99
outliers.
10 1 0.01 1

16. In 2000 the mean age of a sample of females
Example in the U.S. population was 37.8 years with a
standard deviation of 21.8 years and the mean
age of a sample of males was 35.3 with a
standard deviation of 18.4 years.
In relation to the rest of their sex, which is
older, a 48 year old woman or a 45 year old
man?

17. Characterizing a distribution
1. Center, mean/median/mode
2. Skew
3. Spread

18. Characterizing a Data Distribution

19. Characterizing a Data Distribution

20. Characterizing a Data Distribution

21. Characterizing a Data Distribution

22. Characterizing a Data Distribution

23. Characterizing a Data Distribution

24. Characterizing a Data Distribution

25. Characterizing a Data Distribution

26. Characterizing a Data Distribution

27. Characterizing a Data Distribution
Example: For each distribution described below, discuss the
number of peaks, symmetry, and amount of variation you
would expect to find.
- The salaries of actors/actresses.
- The number of vacations taken each year.
- The weights of calculators stored in the math library – half
are graphing calculators and half are scientific calculators.

28. HOMEWORK
2.13 #s 4a, b, c, 7, 10, 12, 13a, b, d, e, f, also construct a line
graph for the data from Publisher A and Publisher B, 16a part
i and iii, 16b, 21, 29, 30, 31