Download ap statistics notes – chapter 2 - Hatboro

Name _______________________________
AP STATISTICS CHAPTER 2:
Consider the following data and graph concerning
heights of freshmen boys:
Heights of Freshman Males
HeightIn... Percent...
<new >
=
1
64
3
2
65
8
3
66
13
4
67
14
5
68
16
6
69
15
7
70
11
8
71
8
9
72
4
10
73
4
11
74
2
12
75
1
4
13
76
1
2
Line Scatter Plot
Heights of Freshman Males
18
16
PercentOfFreshmen
14
12
10
8
6
0
64
What percent of freshmen have heights below 70
inches?
What is the median height of a freshman boy?
DEFINITION: The pth percentile of a distribution
is the value such that p percent of the observations
fall at or below it.
What is the 30th percentile of this distribution?
What is the 90th percentile?
At what percentile would a student of height 71
inches fall?
An OGIVE, or a relative frequency graph allows
us to view the relative standing of individual
observations. The y-axis in this type of graph tells
the relative cumulative frequency for the distribution.
Create an ogive for the height of freshmen males data
set.
SUMMARY/QUESTIONS TO ASK IN CLASS
66
68
70
72
HeightInches
74
76
78
Name _______________________________
AP STATISTICS CHAPTER 2:
Class Notes:
You will download a list of salaries of CEO’s from
59 small businesses (in thousands of dollars) into
your calculators. Give the mean and standard
deviation of this data, and create a boxplot. Describe
the shape of the distribution.
Consider the following changes to the data. Use your
graphing calculator to again determine the mean and
standard deviation, and describe the shape of the
distribution. Create side-by-side boxplots to display
the distribution.
1. The salary of each CEO is increased by 80
thousand dollars. (Use L2)
2. The salary of each CEO rises 30%. (Use L3)
3. The salary of each CEO falls 40%, but then rises
$20,000. (Use L4)
How do changes to a data set, through addition,
subtraction, or multiplication, affect the mean and
standard deviation of a distribution?
LINEAR TRANSFORMATION: A linear
transformation changes the original variable x into
the new variable xnew given an equation by the form:
xnew = a + bx .
Effects of a:
Effects of b:
Effects on the shape of the distribution:
SUMMARY/QUESTIONS TO ASK IN CLASS
Name _______________________________
AP STATISTICS CHAPTER 2:
DENSITY CURVES AND THE NORMAL
DISTRIBUTION
The histogram to the right represents the final grades
for Mr. E’s Calculus classes.
1. What proportion of students had scores below 70?
2. What proportion of students had scores between
75 and 100?
As data sets become larger, we can draw a curve
which describes the overall pattern of the distribution.
1. About what proportion of this curve lies below
70?
2. About what proportion of this curve lies between
70 and 75?
3. If the proportions represented by each bar in the
histogram were equal to the area of each bar, then
what is the total area under this curve?
Steps in exploring quantitative data:
Density Curves:
SUMMARY/QUESTIONS TO ASK IN CLASS
Name _______________________________
AP STATISTICS CHAPTER 2:
SYMMETRIC AND SKEWED DISTRIBUTIONS
Locate the mean and median in these density curves:
NOTATION FOR MEAN AND STANDARD
DEVIATION
Mean
Standard
Deviation
SUMMARY/QUESTIONS TO ASK IN CLASS
Name _______________________________
AP STATISTICS CHAPTER 2:
NORMAL DISTRIBUTIONS
Words which describe a normal distribution:
The density curve for a normal distribution is
described by giving
The Empirical Rule: also known as
The distribution of Iowa Test of Basic Skills (ITBS)
vocabulary scores for 7th grade students in Gary,
Indiana, is close to Normal. Suppose the distribution
is N(6.84, 1.55).
a) Sketch the Normal density curve for this
distribution.
b) What percent of ITBS vocabulary scores are
less than 3.74?
c)
What percent of the scores are between 5.29
and 9.94?
SUMMARY/QUESTIONS TO ASK IN CLASS
Name _______________________________
AP STATISTICS CHAPTER 2:
The height of a giraffe can be described by a normal
distribution. Mean,  = 204 inches with a standard
deviation,  = 5.5 inches. Draw a normal curve to
represent this information.
 What percent of giraffes are taller than 215
inches?
 What percent of giraffes are shorter than 204
inches?
 What percent of giraffes are taller than 198.5
inches?
 A height of 209.5 inch corresponds to what
percentile of giraffe height?
A student states that he got a 640 on both the verbal
and math sections of the SAT. The student stated, “I
feel stronger in math, so I don’t understand what
went wrong.”
After researching the College Board’s website the
following was found:
Math:  = 455,  = 100
Verbal:  = 500,  = 85.
Does this imply that the math score is actually better
or worse? Explain.
SUMMARY/QUESTIONS TO ASK IN CLASS
Name _______________________________
AP STATISTICS CHAPTER 2:
STANDARD NORMAL CALCULATIONS
The standard normal distribution is ________
What if we know that data is distributed normally,
but has a mean and standard deviation other than 0
and 1?
allows us to
change the units so that they can be compared with
the standard normal distribution.
Given: 1)
2)
3)
The standardized value of x is given by:
This new value is called the :
Ex: Former NBA star Michael Jordan is 78 in. tall,
while WNBA player Rebecca Lobo is 76 tall. Men’s
heights have a mean of 69 in, and a standard
deviation of 2.8 in. Women’s heights have a mean of
63.6 in, and a standard deviation of 2.5 in. Which
player is relatively taller? In other words, which
player is taller in comparison to their gender?
Former NBA player Mugsy Bogues is 63 in. tall.
Whose height is more “unusual”, Mugsy’s or
Michael’s?
SUMMARY/QUESTIONS TO ASK IN CLASS
Name _______________________________
AP STATISTICS CHAPTER 2:
Find the proportion of observations from the standard
Normal distribution that are between -1.25 and 0.81.
How to solve problems involving normal
distributions:
 State:
 Plan:
 Do :
 Conclude :
When Tiger Woods hits his driver, the distance the
ball travels can be described by N(304, 8). What
percent of Tiger’s drives travel between 305 and 325
yards?
HOMEWORK
Consider babies born in the “normal” range of 37 to
43 weeks of gestation. Extensive data supports the
assumption that for such babies born in the U.S.,
birth weight is normally distributed with a mean of
3432 g, and a standard deviation of 482 g.
1: What is the probability that the birth weight of a
randomly chosen baby of this type is less than 4000
g?
2: What is the probability that the birth weight of a
randomly chosen baby of this type is more than 3000
g?
3: What is the probability that the birth weight will
be between 3000 and 4000 g?
4: What is the probability that the birth weight will
be between 2500 and 3500 g?
5: What is the 30% percentile of babies’ weights?
What is the interquartile range?
SUMMARY/QUESTIONS TO ASK IN CLASS
Name _______________________________
AP STATISTICS CHAPTER 2:
SUMMARY/QUESTIONS TO ASK IN CLASS
Name _______________________________
AP STATISTICS CHAPTER 2:
SUMMARY/QUESTIONS TO ASK IN CLASS