Transcript MM150 Unit 8 Seminar Definitions Statistics

MM150 Unit 8
Seminar
Definitions
Statistics - The art and science of
gathering, analyizing, and making
predictions from numerical information
obtained from an experiment.
Data - The numerical information obtained.
Descriptive Stats - Concerned with the
collection, organization, and analysis of
data.
Inferential Stats - Concerned with making
generalizations or predictions of the data.
Population - All items or people of interest.
Sample - A subset of the population.
Experiment
• A jar with 90 blue marbles and 10 red
marbles
Random Sampling
- Each item in the population has an equal
chance of being selected.
The best time to use random sampling is
when all items in the population are
similar with regard to the characteristic we
are concerned with (ie. different colored
golf balls)
Best practices: Use a random number
generator or a table of random numbers.
Systematic Sampling
- obtaining a sample by drawing every nth
item with the first item determined by a
random number.
What to watch for:
(1) The list from which the systematic
sampling is taken must contain the entire
population.
(2) The population is comprised of items
where every nth item is made/inspected
by the same entity.
Cluster Sampling
- A random selection of groups of units. Also
called an area sample because it can be
based on geography.
Stratified Sampling
- A population is divided into parts, called
strata, to make sure each stratum is
selected from. Some knowledge of the
population is needed to complete this type
of sampling.
Convenience
Sampling
- Using data that is easy obtained.
Things to consider:
(1) May be only information available
(2) Limited info is better than none
(3) Can be extremely biased
Frequency
Distribution
• A listing of the observed values and the
corresponding frequency of occurrence
of each value.
Frequency Distribution Example
Twelve students recored the number of
siblings they have.
0, 1, 2, 3, 1, 1, 0, 3, 2, 2, 1, 0
Number of
Frequency
Siblings
0
3
1
4
2
3
3
2
Note:
3 + 4 + 3 +2 = 12
Rules for Data Groups By Classes
(1) The classes should be of the same
“width.”
(2) The classes should not overlap.
(3) Each piece of data should belong to
only one class.
*A frequency distribution should be
constructed with 5 - 12 classes.
Frequency Distribution with Classes
A professor wants to construct a frequency
distribution for end-of-term grades.
We must determine upper and lower class
limits. One way that makes sense is
Lower
Class
Limits
90-99
80-89
70-79
60-69
50-59
40-49
30-39
20-29
10-19
0-9
Upper
Class
Limits
Class Width is 10.
In 90-99, there are 10 data scores:
90, 91, 92, 93, 94, 95, 96, 97, 98, 99
Subtract Consecutive Upper Class Limits:
59-49 = 10
Subtract Consecutive Lower Class Limits:
20-10 = 10
Circle Graph Example
32 people are interviewed to determine
their favorite movie genre. Below are the
results.
9 Action
16 Comedy
7 Drama
To construct the circle graph, we must
find the measure of the central angle
for each section of the circle graph.
The circle will be divided into 3
sections.
Circle Graph Con’t
Genre
No. of
Percent of Total
People
Measure of
Central Ang
Action
9
9/32 * 100 = 28.12%
0.2812 * 360 = 101.23
Comedy
16
16/32 * 100 = 50%
0.5 * 360 = 180
Drama
7
7/32 * 100 = 21.87%
0.2187 * 360 = 78.77
Circle Graph Con’t
Comedy
Action
Drama
Stem and Leaf Plot Example
Construct a stem and leaf plot for the following
data scores:
98, 85, 99, 78, 81, 77, 90, 74, 72, 81, 88, 92, 99
7
8
9
7 2 4 7 8
8 1 1 5 8
9 0 2 8 9 9
8 | 1 represents 81