# Analysis Modeling & Simulation

## Teaching data literacy: Module 3

Analysis, Modeling & Simulation: Static data analysis

### Static data analysis

Analysis is the final stage of the data management cycle. Analysis may be static or dynamic. This module discusses each of them. Static analysis measures statistical characteristics of a single dataset covering a fixed time period. For K-8 students, an introduction to static analysis of data is an appropriate final step in the study of data literacy. Static analysis has three steps:

1. Data representation
2. Elementary statistics
3. Computation and interpretation

A dataset can be as simple as a list of cars in a parking lot sorted by color and as complicated as a record of all the trades in Alphabet (Google) stock on a single day. There are many ways to extract information from a dataset. It is essential to choose methods and tools for analysis that match the scale and complexity of the data as well as the skill sets of the analysts. Young elementary students will benefit most from simple exercises that require nothing more than paper and markers. They can learn a lot from very small datasets that they construct themselves. In higher grades, it is appropriate to introduce technological tools that allow students to perform computations and represent data in ways they cannot easily do by hand. The emphasis should always be on the skills students are learning, not on the tools they use to exhibit those skills. The tools will change over time as technology advances. The skills are foundational and permanent.

#### Data representation

Learning outcome
Students learn three ways to present data and statistics derived from it
As discussed in Module 2, not all data is numerical; but a lot of it is. This step in the process of data literacy applies primarily to quantitative data that is generally summarized and presented in tables, charts, and graphs.
A. Describe the different uses of each type of display
1. Tables are used to present numbers themselves in ways that are easy to read, understand, and interpret.
2. Charts are used to compare categorical data based on some kind of sorting criteria. For example, a chart might be used to show populations of different states.
3. Graphs are used to present time series of data. For example, a graph is an excellent way to view the number of wins teams have in a sports league over time.
B. Give students several examples of each type of representation and let them discuss why each example is or is not a good way to represent particular data. As they become familiar with the three displays, they should observe that it I often possible to present the same information in different ways, and that no one way is usually clearly best. A final choice depends in application, the time available to work on it, and the end use.

#### Elementary statistics

Learning outcome
Students learn basic statistical concepts
With a few exceptions, this step generally applies to students in middle school and above. Elementary students should work with the concepts without worrying about what they are called or how they are computed. For example, very young students can collect numerical data and plot it in bar graphs to learn the concept of a distribution. They can learn about averages and observe variations in distributions without learning the technical terms that describe them or the computations used to compute them. For older students, instructors must select concepts listed in the tasks below that correspond to students' level of mathematical knowledge.
A. Define some or all of the following elementary statistics. Defining them does not require teaching students how to compute them. Because students can always use software to compute these quantities, it is more important that they understand when and how to use each of them than it is that they know how to compute them.
1. statistical distribution, mean (average), variance, standard deviation, skewness, kurtosis, correlation coefficient
B. Introduce the concept of ordinary least squares (OLS) regression. Since an understanding of the mathematics of regression requires a knowledge of linear algebra that is usually taught only in college, stick to the concepts and provide examples from spreadsheets that perform the calculations. The key point is simply that regression is a technique that allows us to identify correlations between different datasets. Be sure to define the following regression concepts.
1. dependent variable, independent variable, parameter, t-statistics, F-statistics, R-squared

#### Computation and interpretation

Learning outcome
Students learn to compute and interpret statistics from data