# Simple Statistics

ANALYSIS - Analyze lab data using simple statistics.

## Learning Objectives

You should be able to:

## Basic Statistical Parameters: Sample Mean and Sample Standard Deviation

Generally, engineers assume data is “normally distributed" or that it follows a Gaussian distribution. In graphical 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. Their formulas are provided here along with an example calculation. They are depicted in Figure 1.

## An Example

What would happen if the sample were 3, 3, 4, 4, 4, 5, 5?

Let's use Excel to help:  Figure 1. Depictions of accuracy and precision and relationships to statistical measures of mean and standard deviation.

We often want to compare the results of an experiment to an expected value, which could be a published design value like a material strength or resistor rating. The expected value could also be the result of a previous measurement or the result of some sort of benchmark test. The source of the difference we calculate will depend on the nature of both the expected value and the way we conducted the experiment.

## References

Vardeman & Jobe (2023) Basic Engineering Data Collection and Analysis (a free open educational resource)

Probability and Statistics E-Book