## Actuarial_answers.pdf - Section 2: Using Histograms in the real world

*Actuarial_answers.pdf*

# Histogram activity

Lesson 11 of 23

## Objective: The students will be able to understand that histogram is similar to a bar graph and be able to define mean and know how to apply it to a histogram.

## Big Idea: Students will see how an actuary uses histograms to analyze the frequency of events to determine risk.

*85 minutes*

#### Do Now

*10 min*

Watch a short video clip about Hurricane Katrina. I’m using this video clip to provide some background knowledge for students that may be unaware of what flooding does and why there is a need to keep tract of this data monetarily.

*expand content*

Read a short article about actuaries. After the students have completed the article, have them partner up to make a list of information learned about the actuary’s job. Once everyone has their list, you can do an “I have that” to go over list.

Resource: Actuary’s job description

To start the lesson, ask students about histograms.

What do they tell us?

How are they like a bar graph?

How are they different?

Which measure of central tendency can be found in a histogram?

Once you have reviewed this data display ask students to sketch the following example: A histogram showing the number of books read during several months. Allow students time to sketch their display. Once complete, do a **Hands Up, Stand UP, Pair up** to discuss sketches. Students should be instructed to look for differences in displays and decide if the differences change the way the data looks and/or if the data is still represented correctly **(MP3)**

Next, review the job of an actuary. Explain to students that actuaries can use histograms to compare ranges of data – ex., about populations – and graph the mean.

Review the definition of mean and explain that in this activity the mean represents the single amount of money each person filing a claim would have to pay so that the total amount would cover the costs of all claims, regardless of individual claim amounts. For example, if 5 different people have the following claim amounts: $10, $15, $25, $30, $100 (have the students calculate the mean) Ask the students what this number tells us? (looking for students to say that $36 would be the average amount people would have to pay so that all costs would be covered)

Distribute the Histograms Manage a Flood of Data worksheet. Allow students time to look over the sheet without working. Specifically, draw their attention to the table and ask them what information is being displayed in the table. Then, ask students what they are being asked to do? (create a histogram)

What do they notice about the histogram that they may not have seen before? (there is a break in data between 10,000 and 100,000)

Will this graph be misleading because of the break in data? (depends on how the break is shown on the graph)

Give students time to complete the activity worksheet. When they are done, have students partner up to share their responses. I always make sure students know that when sharing response and there isn’t a similar answer, they must go over through their thinking with their partner to decide if their response is accurate or not.

*expand content*

#### Closure

*15 min*

Use the questions from the activity sheet to close up this lesson. The students have already partnered up to get feedback from their peers. So to use this as whole group discussion will be interesting to hear their responses.

*expand content*

*Responding to Michelle Schade*

https://en.wikipedia.org/wiki/Histogram

I have seen many websites, and even textbooks, claiming that it is used for large amounts of grouped data. However, the only reason we would create such an interval is if an exact measurement cannot be made (this being the definition of continuous data). There is no inherent reason to group data, even at a large scale, except if it is continuous data. For example, when asking what frequency did the height of 185.547455224....cm occur, the answer would always be 1. However if we were to bin all 185cm<x<186cm then we can get a frequency higher than 1.

| 2 months ago | Reply*Responding to Duncan McKay*

Duncan,

That is an interesting perspective and one I have not encountered. It is my understanding (through research and support from textbooks) that a Histogram is used when there is a large amount of data that needs to be grouped in intervals. I'm not invalidating your statement, but what I'm suggesting is that it may be too difficult for 6th grade students to understand the difference between discrete and continuous data. I'm interested to hear your thoughts on how you present it to your class.

Thank you for making me think today!

| 2 months ago | Reply

*Histograms are only used for continuous data. Monetary claims cannot be infinitely measured so they are not continuous data. Therefore, this is not a histogram. Having said that, this is a great lesson plan and I wishhh so badly I could give it to my students. | 2 months ago | Reply*

*Responding to Michelle Schade*

Thanks so much for the reply and help with finding the video on youtube, Michelle. Great hook for the lesson! :)

| one year ago | Reply*Responding to Iris Harrell*

https://www.youtube.com/watch?v=HbJaMWw4-2Q

I found it on youtube.

| one year ago | Reply

Hi, Michelle. I'm very interested in looking into this lesson. I seem to be having trouble with accessing the video clip of Hurricane Katrina. Can you please advise?

Thank you,

Iris Harrell

Santa Rosa County School District, FL

| one year ago | Reply

really nice lesson and practical application... our high schoolers will appreciate this

| 2 years ago | Reply*expand comments*

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