##
* *Reflection: Developing a Conceptual Understanding
Dispersion of Data (Day 1 of 2) - Section 1: Warm Up

Standard Deviation is an important concept when presenting the Spread of the Data. I have found a simple way to present standard deviation in the video below by the AP Stat Guy. I present the method myself, but you could show the video as well.

He presents it in a simple, straight forward way with low numbers. I think it helps students not only develop a conceptual understanding standard deviation, but increases the rigor when they do understand the meaning behind the formula.

The students will use technology most of the time to find standard deviation, but I want them to have an understanding of the concept.

*A nice simple way to introduce Standard Deviation*

*Developing a Conceptual Understanding: A nice simple way to introduce Standard Deviation*

# Dispersion of Data (Day 1 of 2)

Lesson 6 of 10

## Objective: SWBAT describe the spread of the data based on interquartile range, range, outliers, variance, and standard deviation.

## Big Idea: To understand the meaning of dispersion(spread of the data) and to gain the correct vocabulary to describe it.

*50 minutes*

#### Warm Up

*15 min*

I begin the lesson with this Warm Up. I expect the Warm Up to take about 10 minutes for the students to complete and for me to review with the students. In this Warm Up, I provide students with a set of data of free throw percentages of top NBA players.

In this lesson, students will be finding the following to describe the Dispersion (spread) of the data:

1. Range

2. Interquartile Range

3. Outliers/Gaps

4. Variance

5. Standard Deviation (of a sample)

In this Warm Up, I ask students to find the Range and Interquartile Range to describe the spread of the data. Students have previously learned to find Range and Interquartile Range, so the Warm Up should be a review. After the Warm Up, we will continue to use the same set of data through the next section of this lesson. In the next section of this lesson, we will use the other three ways given above to describe Dispersion.

#### Resources

*expand content*

#### Power Point

*20 min*

After reviewing the Warm Up with the students, I hand each student a copy of the Power Point for them to use to write notes. We continue using the data from the Warm Up of the free throw percentages of the top NBA players. I project the Power Point on the Board and quickly review the formulas for Range and Interquartile range that we already found in the Warm Up. Then we begin discussing Outliers, and move forward to Variance, and Standard Deviation.

I demonstrate the work that I did with the students on Dispersion in the video below.

*expand content*

#### Partner Work

*15 min*

In the closure of today's lesson, I assign each set of table partners an additional data set on the salaries of military personnel. I instruct students to describe the dispersion of the data using all of the different ways that we have learned today.

This includes:

1. Range

2. Interquartile Range

3. Outliers/Gaps

4. Variance

5. Standard Deviation

Students use the remaining of the period to begin working on the data set. This is a two day lesson, and students will complete the activity at the beginning of the period the following day.

*expand content*

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Organizing and Calculating Data with Matrices
- LESSON 2: Introduction to Statistics
- LESSON 3: Outliers and their Effect on the Central Tendencies
- LESSON 4: Dot Plots, Box Plots, and Histograms! (Day 1 of 2)
- LESSON 5: Dot Plots, Box Plots, and Histograms! (Day 2 of 2)
- LESSON 6: Dispersion of Data (Day 1 of 2)
- LESSON 7: Dispersion of Data (Day 2 0f 2)
- LESSON 8: What is the Shape of the Data and What Can We Infer?
- LESSON 9: Analyzing Box and Whisker Plots in a Real World Context
- LESSON 10: Compare Two Data Sets Using Box and Whisker Plots