Data Analysis, Probability, and

Algebraic Reasoning

EDU 592 Class 4

Data Analysis and Probability

The possible occurrence of a future event, compared to the chance of its nonoccurrence, can be characterized as impossible, less likely, equally likely, more likely, or certain. To determine the likelihood of an event along this continuum is to determine the probability of its happening.

01

Data Analysis and Probability

Data sets can be analyzed in various ways to provide a sense of the shape of the data, including how spread out they are centered (mean, median, mode).

Leveling the Bars

7 6

4

2 1

Leveling the Bars

The same cubes rearranged into equal stacks.Their height is the mean value of the bars in the

previous slide.

Data Analysis and Probability

• The same set of objects can be considered in different ways, leading to the creation of different classifications. A single object can belong to more than one class.

• Data are organized so as to help with the making of decisions or inferences or the development of new ideas about situations or the populations from which the data are drawn.

Algebraic Reasoning

• Logical patterns exist and are a regular occurrence in mathematics. They can be recognized, extended, or generalized. The same pattern can be found in many different forms. Patterns are found in physical and geometric features as well as in numbers.

^ ^ * ^ ^ ^ * ^ ^ ^ ^ * ^ what comes next?

Algebraic Reasoning

• Symbolism is used to express generalizations of patterns and relationships.

5 + 7 = + 8

5 + 7 = x + 8

Algebraic Reasoning• Variables are symbols that take the place of

numbers or ranges of numbers. They have different meanings depending on whether they are being used as representations of quantities that vary or change, representations of specific unknown values, or placeholders in a generalized expression or formula.

2 + a = 5A = l × w

b = a - 3

Algebraic Reasoning

• Equations and inequalities are used to express relationships between quantities.

5 + 4 (1 +2) × 4

Algebraic Reasoning

• Equations and inequalities are used to express relationships between quantities.

5 + 4 (1 +2) × 4

Tilt!