##
* *Reflection: Real World Applications
Dispersion of Data (Day 2 0f 2) - Section 1: Partner Work

Some of the students really struggled with finding the variance and standard deviation of the military data set. The large numbers made it tedious and some of the students were not patient enough to work through the process to get to the final answer.

Most students showed work, but again some did not get to the final answer. The students that used tables and organized their steps seemed to be more successful.

The purpose of this lesson was not for students to find variance and standard deviation by hand, but yet have a deeper understanding of these two words when using the calculator. I think by assigning students to calculations by hand before working the problems on the calculator provides a deeper conceptual understanding.

Also discussing with students that most of the data sets that we will work with is a sample of the population. Rarely can you describe every individual in a whole population.

This lesson also showed students the importance and appropriate time to use technology. Some students are not comfortable with technology, and this shows those students that there is a need for technology at times.

*Real World Data and the Importance of Technology*

*Real World Applications: Real World Data and the Importance of Technology*

# Dispersion of Data (Day 2 0f 2)

Lesson 7 of 10

## Objective: SWBAT find and describe the dispersion of a set of data about military salaries.

## Big Idea: To check the work of variance and standard deviation using a calculator, and be able to support the description with the math.

*50 minutes*

#### Partner Work

*25 min*

This is the second day of a two-day lesson, so students continue working on thePartner Activity that I assigned the previous day. I assigned students to work with their table partner with a set of data about military salaries. Students are to work by hand to find and describe the spread of the data using:

1. Range

2. Interquartile Range

3. Outliers/Gaps

4. Variance

5. Standard Deviation

Students are to do all of the calculations by hand. They may use the Graphing Calculator for arithmetic operations like squaring, however they are to do the other calculations by hand. Students are to write out the formulas and show all of their work.

Here are some student work samples shown below.

- These two samples, student one and student two, show answers given. Both students show complete work, but I do not provide it here.
- This is a sample of the first three problems. Most of the students were able to get the first three problems correct.

Some of the student work is difficult to see, student one has all of the calculations correct except he or she states that there are no outliers. Student two only has one correct answer and that is the range of the data set. When looking at the final sample, this student also indicates that there is no outlier.

Students seemed to be confused with how to test for the outlier using the IQR* 1.5. Students will need further assistance with this test.

*expand content*

#### Calculator Activity

*15 min*

After providing students about 25 minutes at the beginning of the period to complete their description and supporting math problems for the military data, I review their work with the TI-Nspire Cx calculator. I have students follow along with me using their calculators as well to check their work. I walk around to quickly assess that all of the students have the statistics on their calculator for this univariate data set.

The students should get the following answers to show the spread of the data.

1. Range= Max-Min= 214,120 - 110590=**$103,530**

2. Interquartile Range= Q3-Q1=158560-111870=**$46690**

3. IQR * 1.5= 70,035

Outlier > 113,180 + 70035= $183,215

Outlier< 113,180 - 70035=$43, 145

**So there are two outliers, they are the two highest salaries of $186,044 and $214,120. **

4. Variance= **$1,439,476,987**

5. Standard Deviation of the Sample= **$37,940.44**

I model finding Standard Deviation for a Sample on the TI-Nspire Cx in the video below.

*expand content*

#### Self Reflection

*10 min*

After students have checked over their work, I want them to Self Reflect using a sheet that I provide each of them. I want them to write comments in the box provided on the sheet of any misunderstandings or questions they may still have to clear up.

I also want each of them to focus on the mistakes that they made. Was their mistakes in applying the formula correctly, an arithmetic error, etc. . I ask that students be specific in their self-feedback. Even though they worked with a table partner for the Partner Activity, I want each individual student to provide comments and feedback about their own work that they provided.

For students that did not complete the work for the Partner Activity, I want them to provide a reason of why they did not complete it. I also want them to provide comments and feedback on the parts of the assignment that they did complete.

#### Resources

*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