MM150 Unit 8 Seminar. Definitions Statistics - The art and science of gathering, analyizing, and...

MM150 Unit 8 Seminar

DefinitionsStatistics - 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 ExampleTwelve students recored the number of siblings they have. 0, 1, 2, 3, 1, 1, 0, 3, 2, 2, 1, 0

Number of Siblings Frequency

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 ClassesA 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 90-99 80-89 70-79 60-69 50-59 40-49 30-39 20-29 10-19 0-9

Lower Class Limits

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 Example32 people are interviewed to determine their favorite movie genre. Below are the results.

9 Action 16 Comedy 7 DramaTo 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 People

Percent of Total

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 ExampleConstruct a stem and leaf plot for the following data scores:

98, 85, 99, 78, 81, 77, 90, 74, 72, 81, 88, 92, 99

789

7 2 4 7 88 1 1 5 89 0 2 8 9 98 | 1 represents 81