## Pencil test.wmv - Section 2: Histograms and the Mean

# Hilarious Histograms. Analzying and Creating

Lesson 10 of 23

## Objective: The students will be able to create and analzye Histograms.

## Big Idea: The students will be using real life data to create and analyze histograms. They will be surveying their classmates and using data from other grade levels to compare same topic information in a histogram.

*80 minutes*

#### DO NOW

*10 min*

The DO NOW portion of the lesson sets the stage for the learning for the day. The students will be answering the surveying question “how many 12-ounce cans of soda do your classmates consume in a day” . They begin by stating how much they drink, then they decide whether or not they feel their number will be a typical answer. Once this is done, they can survey the rest of the class to determine how many cans of soda are consumed by their classmates. After the data collection is complete, I want the students to see a histogram. We will discuss the components of a histogram (title, bars not separated, frequency and equal intervals, and labels.) While looking at the histogram, ask students if it is necessary that the numbers be equal along the x axis. We’ve already established that numbers need to be equal on the y axis. Next, I will have them compare and contrast the histogram with a bar graph using a venn diagram. Once we have established that a histogram can show numerical data using intervals, I will have the students use their survey question and create their first histogram. **(SMP 1,2,6)**

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#### Histograms and the Mean

*55 min*

Refer back to the survey question about the amount of cans of soda consumed by their classmates. Ask the students to calculate the mean (if needed, review how to find the mean and have them use a calculator) Randomly choose students to explain how they made their calculations. It is fine if students explain it all the same way. Students in the class that are struggling will benefit from the repetition. I’m expecting some students to say that they grouped same numbers together and multiplied by their frequency, while others may have added all numbers together and divided by how many numbers were in the data set. Next, ask the students if they think the mean is a good way to describe the amount of soda their classmates consume? (accept reasonable answers… some may say yes if all data is about the same and some may say no if there is an outlier)

Pass out the grid paper and have the students make a histogram displaying the data collected. (Before creating, I may once again discuss what a histogram needs to have.)As I walk around the room, I’m looking to see if the data along the x axis shows the number of cans, the data on the y axis is the frequency, the bars are connected, intervals are equal and there are titles and labels. Once all histograms are complete, have the students compare their results with a partner. Before cutting out their histogram, have the students estimate the mean and then calculate it.

Next, have all the students cut out their histogram and tell them to balance it on their pencil (the fold should represent the mean). Ask students to tell you what number the fold is on (depending on the survey, the histogram should be balanced on the mean)

Using slide 5, the students will make a histogram of the new data collected for 7^{th} grade. (New graph paper). Ask the students to first estimate the mean (write it down), then ask them to calculate the mean and ask how well did you estimate.

Ask the students how the data compares to their 6^{th} grade data (the histogram for 7^{th} grade is symmetrical, the mean is 2.5 cans per day and the mean does not seem to represent most of the students, who either drank much more or much less than the mean)

Finally, ask them if it would be helpful to compare the data for the two classes using the mean? (this will depend on the data collected for 6h^{h} grade. If there are outliers, then the mean would not be the best way to compare the data)

Again, have the students create a histogram for the 8^{th} grade class. Using all 3 classes, have them compare the data (center, spread, shape, mean and range). We haven’t talked about range in the other data displays, but it may be a good idea to have them look at the spread of the data to determine how to describe the data set. For example, the comparison between 7^{th} and 8^{th} grade would show that there is a small spread of data, while the range for 8^{th} grade is a larger spread which means there may be really large data points pulling up the mean.

Each graph can be cut out and the pencil test can be used to show the mean. (Good visual for those that struggle to determine the mean)

**Tools: Graph paper, calculator, scissors,**

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#### Closure + Homework

*15 min*

** **The students were creating and analyzing histograms in today’s lesson. In order to effectively assess their learning, I’m going to have them write a few sentences comparing the 6^{th} and 8^{th} grade soda consumption using the mean and ranges. Once they have written their thoughts down on paper, I’m going to have them share their responses with a partner. To insure proper communication, have students decide on who will be an A or a B. Have one of them go first. Students that are listening will be instructed that they will need to paraphrase what their partner was telling them after they are done speaking. So, A goes first and reads what they wrote down. The B says, “I like what you said about”. Then they switch turns. A is now listening and B is speaking. A will respond with “I like what you said about” After the partner share and if time permits, allow the students to share whole class.

*This information can be used as whole class discussion or it can be turned in for evidence of student learning. *

**Homework: Histogram homework. (students will be combining their learning of stem and leaf, histograms and line plots to tell how they could estimate the mean). Then they will be describing a situation when the mean could give the wrong impression of the data. **

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- LESSON 1: Statistically Speaking....
- LESSON 2: What Does the Data Tell Us? Describing Data
- LESSON 3: Describing Data Activity
- LESSON 4: Analyze this! Mean Median Mode and Range
- LESSON 5: Analyze This Part 2!
- LESSON 6: What's Your Frequency? Analyzing and Creating Frequency Tables and Line Plots
- LESSON 7: Line Plot Activity
- LESSON 8: Box and Whiskers... Analyzing and Creating
- LESSON 9: Box and Whiskers Activity
- LESSON 10: Hilarious Histograms. Analzying and Creating
- LESSON 11: Histogram activity
- LESSON 12: Mean absolute deviation. What does it mean?
- LESSON 13: What's in your name?
- LESSON 14: Misleading_Leading_Graphs
- LESSON 15: Say it with Stats! Review
- LESSON 16: Bar none. Analyzing and creating bar graphs
- LESSON 17: Bar Graph Activity
- LESSON 18: Analyzing and Creating Circle Graphs
- LESSON 19: Circle Graph Activity
- LESSON 20: Line me up. Analzying and Creating Line Graphs
- LESSON 21: Line Graph Activity
- LESSON 22: Places Everyone. Analyzing and Creating Stem and Leaf Plots.
- LESSON 23: Stem and Leaf Plots_Activity