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* *Reflection: Problem-based Approaches
An Introduction to Histograms - Section 3: Roll Out Histogram Mini Project

# An Introduction to Histograms

Lesson 5 of 21

## Objective: Students will be able to begin working with histograms through categorization, finding flaws, and organizing their own data.

#### Categorization Activity

*15 min*

At the start of class, I hand all of the students an envelope with the “Categorization Activity” cut pieces in each. I ask the students to sort the cut pieces into two piles – they are allowed to determine the grouping. While the students work, I take care of housekeeping details such as attendance and homework checks. The process usually takes the students no longer than a couple of minutes.

After I see that all students have made their categorizations, I hand all of the students 2 sticky notes and ask them to stand up (with their sticky notes and a pencil). I tell them that they must now take their sticky notes to someone else’s desk and look at the two piles that they have created. After inspecting the other student’s work, the student with the sticky notes must write their thoughts on the note and stick it by the pile. I tell them to use the phrases *“I agree with your piles because….” *or “*Did you ever consider…”*

The students must visit 2 different piles AND each pile is not to receive more than 2 sticky notes – this ensures that everyone receives an equal amount of feedback. Finally, we have a class discussion about what the student’s noticed - - which leads us into our opening investigation of basic histograms!

#### Resources

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#### What is a Histogram?

*15 min*

At first glance, histograms look very similar to bar graphs. Both graphs use bars to represent data. The height of a bar corresponds to the relative frequency of the amount of data in the class: the higher the bar, the higher the frequency of the data - - the lower the bar, the lower the frequency of data. But looks can be deceiving! It is here that the similarities end between the two kinds of graphs, and a Venn Diagram really helps the students see the important differences.

The reason that these kinds of graphs are different has to do with the level of measurement of the data. On one hand, bar graphs are used for data at the nominal level of measurement. Bar graphs measure the frequency of categorical data, and the classes for a bar graph are these categories. On the other hand, histograms are used for data that is at least at the ordinal level of measurement. The classes for a histogram are ranges of values.

Another key difference between bar graphs and histograms has to do with the ordering of the bars. In a bar graph it is common practice to rearrange the bars in order of decreasing height. However, the bars in a histogram cannot be rearranged. They must be displayed in the order that the classes occur. Many students aren’t able to come up with this one, and it takes a little teacher prodding! (It is not a difficult observation to make, but one that takes a little critical thinking.)

We conclude this portion of the lesson by discussing what it takes to make a really good histogram. Obviously, there are several non-negotiable, but I press the students for what qualities does an ideal histogram have.

#### Resources

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- UNIT 1: Culture Building Unit - Welcome to the New Year!
- UNIT 2: Exponential and Logarithmic Functions
- UNIT 3: Sequences and Series
- UNIT 4: Statistics: Something for Everyone
- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
- UNIT 7: Trig Tidbits
- UNIT 8: Functions, Problem Solving, and 21st Century Skills
- UNIT 9: Polynomials and Problem Solving
- UNIT 10: Probability
- UNIT 11: Imagine This! Imaginary and Complex Numbers
- UNIT 12: Let's Explore Radicals!

- LESSON 1: Statistics - Opening Activities and Discussion
- LESSON 2: Role Play PLUS Flaws and Fallacies in Statistical Thinking
- LESSON 3: Flaws and Fallacies (cont.) AND Types of Data
- LESSON 4: Stepping into Box Plots
- LESSON 5: An Introduction to Histograms
- LESSON 6: Using Excel to Create a Histogram
- LESSON 7: A-Mazing Inferential and Descriptive Statistics!
- LESSON 8: What does the Bell Curve SOUND like?
- LESSON 9: The HOW and WHY Behind Standard Deviation
- LESSON 10: A Second Dose of Standard Deviation
- LESSON 11: Straight Walkin' With Statistics - Day #1
- LESSON 12: Straight Walkin' With Statistics - Day #2
- LESSON 13: Straight Walkin' With Statistics - Day #3
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- LESSON 20: Teaching Numbers and Excel
- LESSON 21: Muddying the Waters: Formative Assessment Lesson