Chapter Two
Data
What are Data?
Data are values along with their context Data are information collected in a context Values, by themselves, are meaningless Data should answer the "Five W's"
Who, What, When, Where, Why, sometimes How
Data Table
Stat 101 Lecture 40
Categorical Data
National Opinion Research
Centers General Social Survey
In 1996 a sample of 1895 adults in
the U.S. were asked the question
When is premarital sex wrong?
The participants were also asked
with what religion they were
Stat 101: Lecture 8
The Standard Deviation
as a Ruler
A student got a 67/75 on the first exam
and a 64/75 on the second exam. She
was disappointed that she did not score
as well on the second exam.
To her surprise, the professor said she
actually did be
Stat 101 Lecture 10
Scatter plots and Association
Statistics is about variation.
Recognize, quantify and try to
explain variation.
Variation in contents of cola cans
can be explained, in part, by the type
of cola in the cans.
1
Scatter plots and Associ
Stat 101 Lecture 12
Algebra Review
The equation of a straight line
y = mx + b
m is the slope the change in y over
the change in x or rise over run.
b is the yintercept the value
where the line cuts the y axis.
1
y = 3x + 2
15
10
y
5
0
5
10
15
5

Stat 101 Lecture 14
Residual Standard Deviation
se =
( y y )2
n2
We divide by n 2 because we have
estimated two quantities, the slope and
the intercept.
1
(r)2 or R2
The square of the correlation
coefficient gives the amount of
variation in y, that is
Stat 101 Lecture 13
Line of Best Fit
There are lots of straight lines that
go through the data.
The line of best fit is the line for
which the sum of squared residuals
is the smallest the least squares
line.
1
Line of Best Fit
y = b0 + b1 x
Least square
Stat 101: Lecture 9
From Percentiles to Scores
What octane rating corresponds to
the 25th percentile?
Draw a picture.
The 25th percentile is how many
standard deviations away from the
mean?
1
0.3
Density
0.2
25%
0.1
0.0
85
90
95
100
Octane Rating
2
Sta
Stat 101: Lecture 7
Size of Diamonds
Size of Diamonds (carats)
Frequency
15
10
5
0
0.1
0.2
0.3
0.4
Size (carats)
1
Five Number Summary
Maximum
0.35
Q3
0.25
Median
0.18
Q3
0.16
Minimum
0.12
2
Box Plots
Establish an axis with a scale.
Draw a box that exte
Stat 101: Lecture 1
What is Statistics?
Statistics is a way of reasoning
about the world around us.
Statistics helps us use data to
make informed decisions.
1
Statistics in a Word
Statistics is about variation.
The world is full of data.
Data exhibit v
Stat 101 Lecture 11
Correlation Coefficient
z
zy
n 1
(x x )( y y )
r=
s x s y (n 1)
r=
x
1
Standardized Values
Lucky Strike
Now
Tar = 24
zx = 2.6
Nicotine = 1.5
zy = 2.1
Tar = 2
zx = 2.1
Nicotine = 0.2
zy = 2.5
2
Nicotine Content vs. Tar Content
Stat 101 Final Exam December 13, 2005
Name: _ Section [1 pt]: E F
INSTRUCTIONS: Read the questions carefully and completely. Answer each question and show work in the space provided. Partial credit will not be given if work is not shown. When asked to exp
Stat 101 Lecture 36
Inference for
1
2
Who? Students at I.S.U. What? Time (minutes). When? Fall 2000. Where? Lied Recreation Athletic Center. How? Measure time from when student arrives on 2nd floor until she/he leaves. Why? Part of a Stat 101 data col
Stat 101 Lecture 39
Example
Alcohol and Reaction Time
Experiment run as a block
design with participants as
blocks.
A pair of reaction times
(seconds) for each participant.
1
Alcohol
Participant
No Alcohol
1
2
3
6.7
7.0
7.0
Difference
Alc No Alc
7.4
0.
Stat 101 Lecture 34
Inference for
What is the mean heart rate
for all young adults?
Use the sample mean heart
rate, y , to make inferences
about the population mean
heart rate, .
1
Sample Data
Random sample of n = 25 young
adults.
Heart rate beats pe
Stat 101 Lecture 33
Inference for
Who? Young adults.
What? Heart rate (beats per minute).
Where? In a physiology lab.
How? Take pulse at wrist for one
minute.
Why? Part of an evaluation of
general health.
1
Inference for
What is the mean heart rate fo
Stat 101 Lecture 22
1
Sampling Distribution of p
Shape: Approximately Normal
Center: The mean is p.
Spread: The standard deviation
is
p (1 p )
n
2
Reeses Pieces
Sampling distribution of p
Shape: Approximately Normal.
Center: The mean is 0.45
Spread:
Stat 101 Lecture 21
Sampling Distribution Models
Population Parameter?
Population
Inference
Sample Statistic
Sample
1
Example
Who? Stat 101 students in Sections A
and B.
What? Number of siblings.
When? Today.
Where? In class.
Why? To find out what pr
Stat 101 Lecture 23
Sampling Distribution Models
Population Parameter?
Population
p
Inference
Sample
p
Sample Statistic
1
Sampling Distribution of p
Shape: Approximately Normal
Center: The mean is p.
Spread: The standard deviation
is
p (1 p )
n
2
Sampl
Stat 101 Lecture 24
About 95% of the time the
sample proportion, p , will be
within
p(1 p)
2SE( p) = 2
n
two standard errors of p.
1
About 95% of the time the
population proportion, p, will
be within
p(1 p)
2SE ( p) = 2
n
two standard errors of p .
2
Co
Stat 101 Lecture 32
1
Population
Shape: Not normal, skewed
right
Center: Mean
= 8.08
Spread: Standard Deviation
= 6.22
2
Sampling Distribution of y
n=5
Shape: Approximately normal
Center: Mean
= 8.08
Spread: Standard Deviation
SD( y ) =
n
=
6.22
Stat 101 Lecture 31
Sampling Distribution Models
Population Parameter?
Population
Inference
Sample Sample Statistic
1
Proportions
So far we have used the sample
proportion, p , to make
inferences about the population
proportion p.
To do this we needed t
Stat 101 Lecture 20
Probability
Subjective (Personal)
Based on feeling or opinion.
Empirical
Based on experience.
Theoretical (Formal)
Based on assumptions.
1
The Deal
Bag o chips (poker chips).
Some are red.
Some are white.
Some are blue.
Draw
Stat 101: Lecture 4
Quantitative Data
For a Statistics project, students
weighed the contents of cans of cola.
In 2000, 24 cans of cola were
weighed (full and empty). The
difference in weight is the weight of
the contents. The units are grams.
1
Weight
Stat 101: Lecture 6
Sample Mean Octane Rating
Total = 3637.9
n = 40
y=
Total 3637 .9
=
= 90 .95
n
40
1
Mean or Median?
The sample mean is the balance
point of the distribution.
The sample median divides the
distribution into a lower and an
upper half.
Chapter 2
Saturday, September 13, 2014
10:41 AM
2.1
Most important rule of data analysis Make a picture  a display of your data will reveal things that you won't see in a table of numbers, a welldesigned display will show the important features and patte
Chapter 3
Saturday, September 13, 2014
10:41 AM
We slice up all the possible values into bins and then count the number of cases that fall into each bin
the bins, with the counts, give the distribution of the quantitative variable and provide building blo
Statistics 101: Lab 1  Chapter 2
In seems like almost everyday, a new poll or survey is published concerning peoples attitudes towards different social behaviors, like premarital sex, gay marriage, or abortion. The topics of these
polls and peoples attit
Statistics 101: Labs 2 and 3  Chapters 3 and 4
1. The idea of variation is fundamental to the understanding of statistics. In this lab, you will
conduct some basic research in biology by measuring five different body parts. To make sure
everyone is measu
1/11
5 Ws of data
Who (cases, rows) what when where why how
Variables with labels as values
 Gender
 Eye color
 Year in school
Rows are cases (who)
Columns are variables (what)
Summarize data with:
Frequency table (basic table)
lists categories and nu