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F4: Data Analysis 1-Simple Statistics

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Learning Objectives

This module is designed to assist engineering instructors in strengthening lab instruction materials so that students should be able to:

  1. Understand that engineers analyze data to learn.
  2. Explain what is meant by data variability and what causes it.
  3. Explain the role of statistics in analyzing data.
  4. Determine basic statistical parameters of engineering data (sample mean and sample standard deviation).

Do Engineers Analyze Data to Learn?

All engineering laboratory work is conducted for one reason and one reason only: to learn something. The process of analyzing laboratory data is the process by which engineers make sense of measured data. It is how engineers learn something totally new, never before known by anyone – or at least not known to the same degree. Students of engineering should have the same experience – they should learn something about how the world works when they analyze experimental data.

What is Meant by Data Variability (Error) and What Causes It?

When engineers perform a laboratory test, they are in essence asking the natural world to give them an answer to their engineering question. Engineers would like to have precise and consistent answers to questions; however, all engineering data has variability. In other words, when we repeat an experiment, we hope to get precisely the same results but usually do not. Variability in data is caused by variations in the test conditions, test specimens, measurement devices, etc. For example, the ambient temperature in the room may change enough during testing to affect the data.

What is the Role of Statistics in Analyzing Data?

Variability that is inherent in all engineering data can result in a lack of clarity for engineers attempting to reach a conclusion – it may not be obvious as to what the natural world is telling us. Statistical analysis allows engineers to make greater sense of variability.

Basic Statistical Parameters: Sample Mean and Sample Standard Deviation.

Generally, engineers assume data is “normally distributed”. In graph form, normal distributions result in a bell-curve with most of the data close to the mean but some data are far from the mean. The sample mean and sample standard deviation are two important statistics used to characterize data:

Sample mean, x = (∑xi)/n

Sample standard deviation, s = {∑(xi – x)2/(n – 1)}1/2

Where xi is the value of the i-th data point and n is the number of data points in the sample.
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