##
* *Reflection: Intervention and Extension
Dot Plots, Box Plots, and Histograms! (Day 1 of 2) - Section 3: Exit Slip

For most of my class activities, I believe in homogeneous grouping. However, during the Statistics Unit, I have began to change my mind. First of all, you need to have someone in the group who is comfortable with their artistic ability to draw the graphs. Then you also need a group member that can verbalize and write about the distribution that they are describing.

Therefore, in this unit, I think students would have more success if higher and lower students are paired together. Peers modeling these skills, as well as the modeling by the teacher, I believe will improve student achievement.

*Students abilities with histograms*

*Intervention and Extension: Students abilities with histograms*

# Dot Plots, Box Plots, and Histograms! (Day 1 of 2)

Lesson 4 of 10

## Objective: SWBAT create a Dot Plot, a Box and Whisker Plot, a Frequency Histogram, and a Cumulative Frequency Histogram using a set of data.

#### Introduction

*25 min*

In the Introduction of this lesson, I have students compare seven different test scores of two different students. I hand each student a copy of the Introduction to work individually. Due to lack of space on the page, students should complete the Introduction on their own paper. I am using the Introduction to access the students' prior knowledge. This should be review for most of the students. I expect the Introduction to take about 25 minutes for the students to complete and for me to review with the class. The time for this activity may vary depending on the level of your students.

Students are to look at the two data sets of test grades and determine the Central Tendencies. Students then are to determine which Central Tendency that each student would want to represent their test scores. The two students given, Peter and Amulet, want the highest percentage to represent their test scores.

Peter will want the mean of 86 to represent his test scores compared to the median and mode of 84 in his data set. Amulet will want the median or the mode of 84 to represent her test scores. The mean of Amulet's scores is 82, and would make her test scores look lower. Both students scored an 84 twice on a test, and therefore had the same mode.

The second question of the introduction has students create a summary of the data of cell phone usage given using a Box and Whisker Plot. The final question asks students to explain the process of creating a histogram for the same set of data used for question two. Students do not have to create the histogram, but just explain the process.

I demonstrate reviewing parts of the Introduction in the video below.

*expand content*

#### Notes

*15 min*

After reviewing the Introduction with the students, I hand each student a page to take Notes on as I present a Power Point. The Power Point is on the Advantages and Disadvantages of Dot Plots, Box Plots, and Histograms. The information that I review in the Warm Up helps students identify these Advantages and Disadvantages as well.

Below, I have listed some possible notes for students on each section:

1. Dot Plots

- use with small data sets
- can be categorical or numerical data
- shows every data point
- shows gaps, clusters, or outliers

2. Box Plots

- can be used for large amounts of data
- summary of the data
- all data points cannot be seen
- mean and mode cannot be identified

3. Histograms

- can be used for large amounts of data
- data represented in intervals
- all the intervals have to be the same size
- intervals can be changed to represent the data better

The students notes may vary. If given numerical data, all of the three graphs are an option. In this lesson, I am trying to present to students which one of the graphs is the best option.

*expand content*

#### Exit Slip

*10 min*

After students finish viewing the Power Point and taking Notes, I hand each student an Exit Slip with about 10 minutes remaining in the period. I use the Exit Slip as a quick formative assessment to check for the ability of each student to select the best graph possible for a set of data. Student are to hand in the Exit Slip before leaving.

In the Exit Slip, I provide students with a set of data representing the number of miles that 20 people travel to work. Several of the students chose the Dot Plot because I think it is the easiest graph to create. However, one of the benefits of using the Dot Plot is that you can see every data point. This is a data set of 20, and the Dot Plot should be used for a small data set. So, this data set is almost too large to use for a Dot Plot.

The Box Plot shows a visual summary of the data, but it is difficult to conclude anything about the data from this graph. When analyzing the graph, fifty-percent of the data points of miles traveled was between 3.5 to 13.5 miles. However, this does not really provide much insight about how many miles people travel to work. Providing other percentages about the Box Plot is also of little help.

The Histogram is the best option if the reader is looking for the miles traveled to be summarized into intervals. The highest bar in the graph represents the mode of the data. When using an interval of three for each bin, it shows that the most common miles people traveled to work is either 0-3, 3-6, or 6-9. The range of the miles traveled to work was one to eighteen miles. There was no person that traveled ten or eleven miles.

I show some of the reasoning on selecting the best graph to represent the data given in the video below.

After reviewing the different characteristics of each type of graph with students, we come to the conclusion that selecting a graph also depends on what part of the data the reader wants to highlight.

*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