Quartiles are values that divide a data set into four equal parts. There are three quartiles, denoted as Q1, Q2, and Q3. Q2 is the same as the median, and it divides the data set into two halves. Q1 divides the lower half of the data (excluding Q2), and Q3 divides the upper half of the data (excluding Q2).

To find the quartiles of a data set, you can follow these steps:

- First, arrange the data in ascending order.
- Find the median (Q2) of the data set.
- To find Q1, calculate the median of the lower half of the data set (the values below Q2).
- To find Q3, calculate the median of the upper half of the data set (the values above Q2).

Consider the following data set: 12, 15, 17, 20, 22, 25, 30, 35, 40, 45

First, arrange the data in ascending order: 12, 15, 17, 20, 22, 25, 30, 35, 40, 45

The median (Q2) is the middle value, which is 22.

The lower half of the data set is 12, 15, 17, 20, so the median of the lower half (Q1) is 16.

The upper half of the data set is 25, 30, 35, 40, 45, so the median of the upper half (Q3) is 35.

Quartiles are used to understand the spread and distribution of a data set. They are particularly helpful when comparing different sets of data. For example, comparing the quartiles of two different test scores can help identify the differences in the performance of the students.

Understanding quartiles is important in various statistical analyses and helps in making informed decisions based on data distribution.

It's important for students to practice calculating quartiles with different data sets to gain a strong understanding of the concept.

Remember, Q1 is the 25th percentile, Q2 is the 50th percentile (median), and Q3 is the 75th percentile.

Now that you understand quartiles, it's time to practice and master the concept through various problems and exercises.

.Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

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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.