The standard deviation is a measure of the amount of variation or dispersion of a set of values. It is a way to quantify the amount of variation or dispersion in a set of data values.

The formula for calculating the standard deviation of a sample is:

**s = √(Σ(x - x̄) ^{2} / (n - 1))**

Where:

- s = standard deviation
- Σ = summation (add up all the values)
- x = each individual value in the data set
- x̄ = the mean of the data set
- n = number of values in the data set

- Find the mean of the data set.
- Subtract the mean from each data point and square the result.
- Find the sum of all the squared differences.
- Divide the sum by (n - 1) where n is the number of data points (this gives the variance).
- Take the square root of the variance to get the standard deviation.

A larger standard deviation indicates that the data points are spread out over a larger range of values, while a smaller standard deviation indicates that the data points are closer to the mean.

Standard deviation is commonly used in various fields such as finance, science, and social sciences to understand the variability of data and make informed decisions.

Understanding and calculating standard deviation is important for analyzing data and making statistical inferences. It provides valuable insights into the spread of data values and helps in making data-driven decisions.

.Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.