Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments (Mr. Wiki).
Job of a Statistician
-Collects numbers or data
-Systematically organizes or arranges the data
-Analyzes the data…extracts relevant information to provide a complete numerical description
-Infers general conclusions about the problem using this numerical description
Uses of Statistics
-Statistics is a theoretical discipline in its own right
-Statistics is a tool for researchers in other fields
-Used to draw general conclusions in a large variety of applications
Two kinds of Statistics
DESCRIPTIVE STATISTICS
Procedures used to summarize and describe the set of measurements.
INFERENTIAL STATISTICS
Procedures used to draw conclusions or inferences about the population from information contained in the sample.
The Objective of Inferential Statistics
- To make inferences about a population from information contained in a sample.
The Steps in Inferential Statistics
- Define the objective of the experiment and the population of interest
- Determine the design of the experiment and the sampling plan to be used
- Collect and analyze the data
- Make inferences about the population from information in the sample
- Determine the goodness or reliability of the inference.
Word Bank
Population
- Well defined collection of objects.
Sample (Relationship to population)
- Subset of population.
Experimental Unit
- Items or objects on which measurements are taken.
Sample (Relationship to experimental unit)
- Set of measurements taken on experimental unit.
Variable
- Characteristic that changes or varies over time and/or for different individuals or subjects under consideration.
Univariate data: One variable is measured on a single experimental unit.
Bivariate data: Two variables are measured on a single experimental unit.
Multivariate data: More than two variables are measured on a single
experimental unit.
Types:
Qualitative variables
- Measure a quality or characteristic on each experimental unit.
Quantitative variables
- Measure a numerical quantity on each experimental unit. It is divided into two:
=Continuous if it can assume the infinitely many values corresponding to the points on a line interval.
Measurement
- Result when a variable is actually measured on an experiment.
Example:
>Variable: Hair Color
>Experimental Unit: Person
>Sample unit: CS Students
>Measurement: Brown, black
Data Distribution
To solve for "How often the value occurred”, you can solve it in 3 ways:
A. Frequency (count how many times a value appears on the data)
B. Relative frequency = Frequency/n
C. Percent = 100 x Relative frequency
where: n= total number of elements in the population/sample
Graphing Quantitative Variables
Dotplots
-The simplest graph for quantitative data
-Plots the measurements as points on a horizontal axis, stacking the points that duplicate existing points.
Example: The set 4, 5, 5, 7, 6
Stem and Leaf Plots
-A simple graph for quantitative data
-Uses the actual numerical values of each data point.
Interpreting Graph
(Source: Yarmouk Univ 2003)
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