Statistics Sta3032 University of Central Florida

Inferential Statistics: used to infer from a sample (subset of data) characteristics of a target population of data from which the sample was drawn

For example:

What is the typical time to complete a Bachelors degree in engineering?
From a sample of 40 students the following is calculated:

Example Cont’d

Thus, infer that for all students the mean time to graduate is 4.32 years, with a variance of +-0.5 years.

Inferential Statistics

The statistical tool used to describe and analyze data depends on the type of data being analyzed.

Two Types of Data

1. Quantitative Data is data
   which represents the
   quantity or amount of
   something, measured on
   a numerical scale

i.e. waiting time, performance time, weight, cost, frequency, etc.

Two Types of Data

2. Qualitative (categorical)
   Data is data which has no
   quantitative interpretation,
   but instead can be classified
   into categories

i.e. types of engineering majors, types of business, location, etc.

Uncertainty

An inference based on sampling a population
is always subject
to uncertainty.

For example:

Earlier we presented calculations from a sample of 40 engineers which indicated that the mean time to graduate was 4.32 years.

Example Cont’d

From another sample we may obtain a mean of
4.56 years.
The true time to graduate may be 4.45 years.

Uncertainty Cont’d

The theory of statistics uses probability to measure the uncertainty associated with inferential statistics.

Uncertainty Cont’d

The probability of observing the characteristics of a specific sample is calculated under specific assumptions about the target population.

Uncertainty Cont’d

The probability is then used to evaluate the uncertainties (i.e., confidence, accuracy) associated with the sample inferences.

Uncertainty Cont’d

Statistics thus enables one to make inferences

(i.e., estimates & decisions about a population based on sample data)

with a known measure of uncertainty (i.e., reliability).

Statistics & Computer Analysis

Most data analysts today
use statistical packages.

Statistics & Computer Analysis

It is important for you to learn how to use these packages in order to facilitate your ability to analyze large data sets.

Statistics & Computer Analysis

Excel will be used to analyze data in this course.
This package was selected due to its ease of use and widespread acceptance in industry.

Excel Labs

There will be approximately 3 computer labs assigned throughout the semester.

Excel Labs

All labs are due 1 week after they are assigned.
Microsofts Excel's statistical functions let you analyze groups of numbers.

Some Excel Functions

Excel functions include, but

are not limited to:

summation = SUM (numbers or range)
averaging = AVERAGE (numbers or range)

Excel Functions Con’d

median calculations = MEDIAN (numbers or range)
mode calculations = MODE (numbers or range)

Excel Functions Cont’d

maximum calculations =MAX(numbers or range)
minimum calculations =MIN(numbers or range)

Excel Functions Cont’d

variance =VAR (numbers or range)
standard deviation =STDEV (numbers or range)

Excel ToolPak

Excel also has an Analysis ToolPak which is a collection of tools which augments Excel's built-in analytical capability.

Excel ToolPak

The ToolPak allows you to:

create histograms
produce rank-and-percentile tables

Excel ToolPak Cont’d

extract random samples from a data set
perform regression analysis
return statistical measures of data sets

Using ToolPak

Before you use an analysis tool, you must organize the data you want analyzed into columns or rows on your worksheet.

Using ToolPak Cont’d

This is your input range.
You can also include a text label in the first cell of a row or column to identify your variables.

Using ToolPak Cont’d

When you use an analysis tool to analyze data in an input range, Microsoft Excel creates an output table of the results.

Using ToolPak Cont’d

If you included labels in the input range (by checking the appropriate dialog box), Microsoft Excel uses them to label data in the output table.

Using ToolPak Cont’d

Microsoft Excel automatically generates data labels for the results in the output table.

General Procedures for using the ToolPak

From the Options menu, choose Analysis Tools.
In the Analysis Tools box, select the tool that you want to use.
Choose the OK button.

General Procedures for using the ToolPak

Type the input range, the output range, and any other options you want.

General Procedures for using the ToolPak

Choose the OK button.
The results of the analysis will appear in the cell range that you designated as the output range.

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