Stat 121: Describing Data
Natasha Mandryk
1
!Visualize distributions with stemplots
!Measures of centre: Median and mean
!Measures of spread: Interquartile range
!Visualize distributions with boxplots
Todays Plan
2
!Discuss measures of spread:
"Interquar
Stat 121: Inference about
Two Population Means
Moore chapter 18
1
inference when is unknown
Confidence intervals
One-sample t test
Matched pairs design
t distributions, degrees of freedom
Critical values Table C
Recall: t procedures
2
Confidence interval
Stat 121
Sampling Distributions
Moore chapter 11
1
KEY WORDS
Sampling distribution
Law of large numbers
Central limit theorem
STUNNING IDEAS
Sampling distributions are
approximately normal
Sample means vary less than
individual observations
Sample means h
Stat 121:
Inference about a Population Proportion
Moore chapter 19
1
Count type data
Divides population into two groups
Smokers and non-smokers
University students and everyone else
Think yes/no: number of yes in a group
Proportion
2
Percentage of Canadia
Fuel economy ratings give the Prius a highway
mileage of 48 mpg. Deborah wonders whether
the actual highway mileage of her Prius is less
than that. She keeps careful records for 3000
miles of highway driving and finds her average is
47.2 mpg. What are her
MAKING SURE CONDITIONS ARE REALLY SATISFIED
REALITY MEETS CALCULATIONS
30
! Study investigates link between community service
and secure relationships
! Sample: 74 students
57 had done service work
17 had not
! Measure attachment to friends: Inventory
Stat 121 Assignment 1 Summer 2013
Assignment Instructions
You may work alone or in groups of up to 3. If you work in a group, submit one paper with all
team member names on it.
Assignments must be submitted in hard copy and stapled.
You may either use SPS
Stat 121:
Inference about a Population Proportion
Moore chapter 19
1
1.
The data are an SRS from the population.
2.
The population is at least 10x larger than the sample.
Ensures that standard deviation of is
1 / .
The sample size n is large enough that t
STAT121
Assignment1
JishengLiu
12862132
1.
a)
Height
DegreePrgm
BA
Mean
Statistic
Std. Error
167.63 1.953
95% Confidence Interval Lower Bound
for Mean
Upper Bound
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Ske
STAT121
Assignment1
JishengLiu
12862132
1.
a)
Height
DegreePrgm
BA
Mean
Statistic
Std. Error
167.63 1.953
95% Confidence Interval Lower Bound
for Mean
Upper Bound
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Ske
Stat 121:
Two Categorical Variables
Moore chapter 22
1
How do we determine
whether there is a
relationship between
education levels and
views on capital
CATEGORICAL
punishment?
VARIABLES
2
Cant calculate z or t statistic
Cant study correlation
Need new pr
Stat 121
Introduction to Inference
Moore Chapter 14
1
a)
Gives a range of reasonable values for the level of
confidence.
b)
Gives a range of reasonable values for the sample mean.
c)
Gives a range of reasonable values for the population mean.
d)
Gives a r
a)
Drawing conclusions about a population mean based on
information contained in a sample.
b)
Drawing conclusions about a sample mean based on
information contained in a population.
c)
Drawing conclusions about a sample mean based on the
measurements in t
Stat 121: Normal Distributions
Which one of the following is a FALSE statement about the
standard normal curve?
a)
b)
c)
d)
Its standard deviation can vary with different datasets.
It is bell-shaped.
It is symmetric around 0.
It has mean = 0.
Standard No
Strong positive
association:
number of
firefighters at a
structure fire
total damage
caused by fire.
Photo credit Flickr/dvs. CC licenced.
Are firefighters bad?
1
Need to take into account to explain the
relationship between x and y
Explanatory variable
Stat 121
Introducing Probability
1
KEY WORDS
4 laws of probability
Normal probability
Sampling distribution
Law of large numbers
Central limit theorem
STUNNING IDEAS
Normal curve is really a
probability curve
Proportions = probability
Sampling distributio
Stat 121 Reading for Chapter 2 Describing Distributions with Numbers
Instructions: Read Chapter 2. Take notes as you go. Bring your notes to class.
Your notes should help you to answer the following:
What does the five-number summary consist of? How is it
Stat 121 Reading for Chapter 4:
Scatterplots and Correlation
Instructions: Read Chapter 4. Take notes as you go. Bring your notes to class.
Try to answer the following:
What is the difference between an explanatory variable and a response variable? Give e
Stat 121 Reading for Chapter 1 Picturing Distributions With Graphs
Instructions: Read Chapter 1, omitting the section on time plots. Take notes as you go. Try the practice
problems at the end.
Your notes should help you to answer the following:
Whats the
Stat 121 Reading for Chapter 3 The Normal Distributions
Instructions: Read Chapter 3. Take notes as you go. Bring your notes to class.
Try to answer the following:
How is a density curve related to a histogram?
Sketch density curves for
1. a symmetric dis
Discuss/compare measures of centre and spread
Compare distributions using centre and spread
Discuss density curves and normal distributions
Estimate proportions of normally distributed populations
Todays agenda
50
s measures spread about the mean
Bigger s
MUDDIEST POINT
1
Count
Minimum Value
Maximum Value
Range
40
5.00
10.00
5.00
Average
Median
Standard Deviation
Variance
8.45
9.00
1.24
1.55
Last days activity statistics
2
Stat 121: Normal Distributions
DENSITY CURVES
5
Whats the difference between
a densi
tinyurl.com/stat121survey
(alternative paper form at front of room)
Class Survey May 2013
Stat 121:
Representing Data
Natasha Mandryk
Flickr: Jerry Oldenettel
Behrs Hairstreak
ID
Capture type easting
northing Plant
date
time
Capture site
12 Initial
316591
What questions
come to mind?
TOASTER
REGRESSION
1
Toast data: what do you see?
2
If a child has IQ 110,
what would you
predict his/her
reading score to be?
3
LINES OF BEST FIT
PREDICTING RESPONSE VALUE FROM EXPLANATORY DATA
4
Which line fits best?
5
Which
Stat 121: Scatterplots and Correlation
Represent data visually: one measurement per
individual
Grouped individuals by categorical variable: compare
distributions of quantitative variable
E.g. Student heights by degree program
Previously in Stat 121.
2
Pl
Stat 121
Introducing Probability
1
Which is a correct interpretation of the statement The
probability that a child delivered at KGH is a girl is 0.50?
a)
Over a long period of time, there will be equal proportions of
boys and girls born at that hospital.
6/4/2013
HOW MUCH DID YOU SPEND
ON COFFEE YESTERDAY?
ANSWER HERE:
Stat 121
Sampling Distributions
Moore chapter 11
http:/tinyurl.com/stat121coffee
1
A random sample of 1600 people across Canada was asked if
they regularly watch a certain television progra
Quiz 1 and Assignment 1 available for pickup
Assignment 2 due in class tomorrow
Lab quiz this week
For tomorrow:
Read ch 89 (qualitative)
Think about how you would design an experiment to test the
effects of marijuana on motivation and productivity in t
Stat 121 Reading for Chapter 5 Regression
Instructions: Read Chapter 5. Take notes as you go. Bring your notes to class.
Try to answer the following:
How are regression and correlation related?
What kinds of patterns or relationships can regression descri