Transcript A statistical population is a set of entities concerning - Stone-Math

Statistics
Statistics
Our objective today:
• Learn about statistics and why
they are important
• Explore how we can gain
information about a population
by examining a sample
population
Statistics
Statistics is the study of the
collection, organization, analysis
of data.
Statistics
A statistical population is a set of
entities concerning which
statistical inferences are to be
drawn.
Examples:
• Population of a school
• A sports team
Statistics
 A statistical sample is a subset
of the statistical population that
should represent the statistical
population.
 A sample is valid only if the
sample is representative of the
population
Statistics
 Random sampling tends to
produce representative samples
and support valid inferences.
Statistics
 Variability – a measure of how far
a set of numbers is spread out.
 Measures of Central Tendency –
relates to the way in which data
tends to cluster around some
value
 Mean
 Median
 Mode
 Range
http://www.youtube.com/watch?v=qpxtBghmvvs
Data Set: 11, 26, 22, 15, 18, 26, 16
Mean
Median
Mode
Range
Data Set: 5, 12, 6, 15, 7, 10, 4, 8
Mean
Median
Mode
Range
http://www.youtube.com/watch?v=1jVZi0cNHls
Statistics
Can you think of any
ways that Statistics are
used in life?
Statistics
Can you think of data
distributions and
statistics kept in sports?
Who cares about these?
Would variability matter
in Tim Duncan’s
earnings?
CAN YOU THINK OF
OTHER SPORTS
STATISTICS ?
Statistics
Statistics
Statistics & Probability
Statistics
Can you think of data
distributions and statistics
kept for music?
Who cares about these?
Would variability matter in
Rihanna’s statistics?
Statistics
Can you think of data distributions
and statistics kept that will effect
your application to college?
Who cares about these?
Would variability matter ?
Statistics
Statistical Data can be
1. Categorical
2. Numerical
Statistics
Categorical Data – data that fall into specific labels or
categories.
Categorical data is data that is defined by words or as
a limited number of answer options.
Statistics
Categorical data is reported in the FREQUENCY. It is
recorded by how many or what percentage fall into
each category.
For example, if you counted the number of each color
of M&Ms found a bag, you may find.
Number
Percent
Green
Yellow
Orange
Blue
Brown
Red
Total
5
14
4
4
19
12
58
Statistics
If you counted several bags, you might find.
Green
Yellow
Orange
Blue
Brown
Red
Total
Bag 1
5
14
4
4
19
12
58
Bag 2
5
15
2
7
15
10
54
Bag 3
3
13
5
5
19
10
55
Statistics
This data can also be
reported in other forms,
such as bar graphs that
show the frequency.
What patterns do you see?
Statistics
The following is actual data of colors found in a
sampling of 30 bags of M&Ms.
• Find the percentage of each color.
• Sketch a bar graph showing the percentages.
Number
Percent
Green
Yellow
Orange
Blue
Brown
Red
92
449
109
90
576
415
Total
1,731
Statistics
40%
35%
30%
25%
20%
15%
10%
5%
0%
30 Bags – Percent of Each Color
Green
Yellow
Orange
Blue
Brown
Red
Do you think the sample of 30 bags have any more
statistical reliability than the earlier sample of 3 bags?
Statistics
Numerical Data – data that are counts or measures.
For example, we count people to find the population of
each state in the United States in order to answer the
question, “How much do state populations vary in
size?”
Statistics
What are other examples of numerical data?
Statistics
In decade from 1901 to 1910, how many immigrants came
from Europe? What else can you say about this decade?
Decade
Immigrants From
Europe
Total
Immigrants
Percent of Immigrants
From Europe
1881–1890
4,735,484
5,246,613
90%
1891–1900
3,555,352
3,687,564
96%
1901–1910
8,056,040
8,795,386
92%
1911–1920
4,321,887
5,735,811
75%
1921–1930
2,463,194
4,107,209
60%
1931–1940
347,566
528,431
66%
1941–1950
621,147
1,035,039
60%
1951–1960
1,325,727
2,515,479
53%
1961–1970
1,123,492
3,321,677
34%
1971–1980
800,368
4,493,314
18%
1981–1990
761,550
7,338,062
10%
1991–2000
1,359,737
9,095,417
15%
Statistics
Categorical vs. Numerical ?
• Age
• Month you were born.
• Weight
• Favorite Singer
• Eye Color
• Height
• Favorite Ice Cream
Statistics & Probability
The school food service wants to increase the
number of students who eat lunch in the cafeteria.
The student council has been asked to conduct a
survey of the student body to determine the
students’ preferences for hot lunch. They are
considering several methods to do the survey.
Statistics
Let’s look at the methods and determine if they
would provide a random sample. Which method
should the council use?
1. Write all the student’s names on cards and pull
them out in a draw to determine who will
complete the survey.
2. Survey the first 20 students that enter the
lunchroom.
3. Survey every 3rd student who gets off a bus.
Statistics
Now, let’s devise a sampling method in our class for
conducting the following surveys.
1. Do 7th Grade Students prefer Coke or Pepsi products ?
2. What is the average shoe size for students at Quail Hollow?