Intro to Data Sciences
Mathematics Curriculum
Statistics is the art and science of deriving meaning from data.
Prerequisite: Algebra 1
(Half Year – 0.50 Credit) - Level 1 or Level 2
This course is designed to provide the background necessary to interpret statistical data. It will include elementary probability and the fundamental statistical method needed to interpret and prepare research materials. Emphasis is placed on gathering and exploring data, relationship between variables, randomness and probability, and using a sample to draw conclusions about a population. Such a study should benefit any student interested in a career in science, business, social science, education, or mathematics. Students will be introduced to Microsoft Excel features as they conclude each unit with an Excel project and/or Case Study. A graphing calculator (TI-83 or TI-84) series is required for this course.
Unit 0: The Process of Statistics – How do we get an unbiased collection of data?
Conceptual Lens: Data Collection
The process of going from a question to a conclusion will be outlined in this unit. Different ways to collect data will be explored. Students will begin to understand the parameters needed to realize the validity of data presented to make informed decisions. They will realize that every part of the statistical process needs to be in place in order to make any reliable conclusions.
Unit 1: Descriptive Statistics – How do we organize and analyze data?
Conceptual Lens: Organization and Analysis of Data
In Unit 1, the students begin to organize and analyze data. Students will be given data and will choose the appropriate displays for the data. Students will make appropriate calculations to summarize the data. Students will then use the displays and the calculations to thoroughly describe the data. Throughout the unit students will understand that data can be analyzed through diagrams and calculations.
Unit 2: Normal Distributions – How can we make use of patterns in nature to make predictions?
Conceptual Lens: The Normal Curve
In this unit, students will be introduced to the normal curve. They will see that it is commonly observed in nature. Students will calculate the proportion of observations on a given interval in a normal distribution. They will also find a point on the curve for a given percentile in the distribution. Ultimately, students will see that many phenomena can be modeled with a normal curve and that allows us to easily make calculations regarding the frequency of an event.
CCSS: S.ID.4
Unit 3: Linear Regression – How can we quantify the relationship between two variables?
Conceptual Lens: Paired quantitative data
In this unit, students will compare two data sets to check for association in a scatter plot. They will learn to identify the types of data where this would be useful to do so and to understand the limitation of this process. The line of regression would be used to both interpolate and extrapolate unobserved data. Students will also use the correlation coefficient and the coefficient of determination to appropriately assign the predictive usefulness of this line. Students will look at a graph of the residuals to see if a linear model is appropriate for the data. Students will also understand the difference between correlation and causation. By the end of the unit, students will determine linear models can be constructed to represent the relationship in the data and predictions can be made based on the model.
CCSS: S.ID.6 - 8, S.IC.6
Unit 4: Probability – How do we determine the likelihood of an event?
Conceptual Lens: Randomness
The idea of probability will be introduced with experiments and simulations and then calculated with basic rules to find probabilities. The probability of an event is the number that measures the likelihood that the event will occur. Probability quantifies the likelihood that something will happen and enables us to make predictions and informed decisions. Two characteristics of objects will be analyzed via a two-way table to see how information about one will affect the likelihood of the other. Models are used to simulate real world decisions, enabling us to make predictions.
CCSS: HSS.CP.A.1-5, HSS.CP.B.6-9, S.IC,A.2
Unit 5: Inference – How can we know the level of certainty in our answers to statistical research questions?
Conceptual Lens: Inference
Students will be introduced to the idea of inference. In this unit, students will make conclusions about a population based on a sample. The unit begins by looking at the distribution of the sample mean; discovering its center, shape, and spread. That is used to create interval estimates of parameters and to calculate the probability of observing the given sample if an initial assumption is true to ultimately draw conclusions. Finally, students will create confidence intervals for the mean and will conduct a hypothesis test for a mean. Students will learn that inferences can be made about a population based on a sample with a stated degree of certainty.
CCSS: S.IC.A.1, S.IC.B.3-6