1. The Shape of Distributions of Data

2. Warm Up
OBJECTIVE: Learn to describe the shape of a distribution of data using appropriate vocabulary.
James kept track of how much he spent on lunch each day for a week, and got the following results: $5, $7, $4, $5, $10, $6, $5
What is the median of this data?
What is the mean of this data?
What is the range of this data?
Alexis asked 10 people what their favorite color is, and got the following answers:
Blue, green, orange, yellow, blue, blue, red, black, red, green
4. Why doesn’t it make sense to find the mean, median, or range of this data?
(5 min) 0-5
In-Class Notes
This warm up is a review to make sure everyone is up to speed with what they have learned so far about statistics.
The fourth question is especially important, because everything they learn today only applies to quantitative data, not qualitative. Make sure you emphasize this before the lesson begins!
Preparation Notes
It might take a little more than 5 minutes for everyone to finish this warm up. It is better to spend a little extra time here, and a little less time somewhere else (perhaps the practice) because these concepts are key to moving on in the study of statistics.
Agenda

3. Launch – Next Step
Lets take a look at the middle names of two classes, and compare their center and spread.
(2 min) 8-10
In-Class Notes
Have students volunteer to answer what the center and spread is for these two graphs.
They will see they have the same center and spread, but these graphs certainly are different.
Click on the word to display the answer.
This slide’s purpose is to show the need for more tools to describe a distribution
Preparation Notes
Many students are used to seeing graphs only in a concrete example. It is good for them to practice analyzing abstract graphs without having to worry about what the statistical question is that the data came from. If any students have any concerns about labeling, tell them this is just an example and we would always title our graph appropriately if we created a bar graph on our own.
Center:
____4_____
Center:
____4_____
____7 - 1 = 6_____
Spread:
Spread:
____7-1 = 6_____
Agenda

4. Launch B
“These bar graphs have the same center and spread, but they are completely different!”
(1 min)
In-Class Notes
Preparation Notes
Agenda

5. Summary – Vocabulary
To accurately describe the shape of a distribution, there is a standard group of vocabulary words that can help us. Copy the following vocabulary words and definitions onto your worksheet.
(1 min) 25-26
In-Class Notes
Have the students write down these vocabulary words in the space provided on the worksheet.
Make sure to explain how the pictures provided are an example of the vocabulary word.
Have them copy the words again into their “vocabulary notebook” if they have one. The extra copying will help them remember the meaning.
Preparation Notes
There are more vocabulary words to describe the shape of a graph, but these are the most common, and will be sufficient for any questions that will be asked.
Agenda

6. Summary – Vocabulary
1. Symmetry: When it is graphed, a symmetric distribution can be divided at the center so that each half is a reflection of the other.
Examples:
(2 min) 26-28
In-Class Notes
Have the students write down these vocabulary words in the space provided on the worksheet.
Make sure to explain how the pictures provided are an example of the vocabulary word.
Preparation Notes
There are more vocabulary words to describe the shape of a graph, but these are the most common, and will be sufficient for any questions that will be asked.
Agenda

7. Summary – Vocabulary
2. Peak: A point on the graph that is higher than the points directly to the left and right.
Examples:
One Peak
Two Peaks
(2 min) 28 – 30
In-Class Notes
Have the students write down these vocabulary words in the space provided on the worksheet.
Make sure to explain how the pictures provided are an example of the vocabulary word.
Preparation Notes
There are more vocabulary words to describe the shape of a graph, but these are the most common, and will be sufficient for any questions that will be asked.
Agenda

8. Summary – Vocabulary
3. Skewed left/right: A graph is skewed left if it is highest to the right, then becomes lower as it goes left. A graph is skewed right if it is highest at the left and lowers as it goes right.
Examples:
Skewed Left
Skewed Right
( 2 min) 30 – 32
In-Class Notes
Have the students write down these vocabulary words in the space provided on the worksheet.
Make sure to explain how the pictures provided are an example of the vocabulary word.
Preparation Notes
There are more vocabulary words to describe the shape of a graph, but these are the most common, and will be sufficient for any questions that will be asked.
Agenda

9. Summary – Vocabulary
4. Uniform: A graph that is evenly spread out, with no peaks.
Examples:
Uniform
(2 min) 32 – 34
In-Class Notes
Have the students write down these vocabulary words in the space provided on the worksheet.
Make sure to explain how the pictures provided are an example of the vocabulary word.
Preparation Notes
There are more vocabulary words to describe the shape of a graph, but these are the most common, and will be sufficient for any questions that will be asked.
Agenda

10. Summary – Vocabulary
Distributions may also have unusual features. The two most common ones are:
6. Gap: An area of the distribution where there are no entries in the data set.
7. Outlier: An element of the data set that is much higher or much lower than all the other elements.
Outlier
Examples:
Gap
(2 min) 34 – 36
In-Class Notes
Have the students write down these vocabulary words in the space provided on the worksheet.
Make sure to explain how the pictures provided are an example of the vocabulary word.
Preparation Notes
There are more vocabulary words to describe the shape of a graph, but these are the most common, and will be sufficient for any questions that will be asked.
Agenda

11. Summary – Looking Back
Let’s go back to the two graphs we looked at earlier. How can we describe them using the vocabulary that we just learned?
(4 min) 36 – 40
In-Class Notes
This time around, the students should be able to easily describe the shapes of the graphs.
Let everyone know they should be as descriptive as possible.
Preparation Notes
There is no completely correct answer. As long as the students are highlighting the main points, it should be evident that they are grasping the concepts.
Hint: Go right down the vocabulary list and identify each one.
Remember – Symmetry, Peaks, Skew, uniform, unusual features.
scaffolding
Agenda

12. Practice – Interactive Classwork
We will now complete the back side of your class work. Describe the shape of each graph with as much detail as possible.
(1 - min) 40-41
In-Class Notes
If you don’t want to display the answers, click “next slide” at the bottom.
Problems 1 and 4 have some extra parts for any students who are up to the challenge. Hit the “Take it further” button to show prompt.
Preparation Notes
Try not to spend too long of a time on these questions, because they can get drawn out. Rather, try and find a fluid, standard way to move
through each exercise with your students, so they can get used to the standard practice.
Agenda

13. Practice Describe the SHAPE of this graph: Symmetry: Peaks:
Skewness:
Uniformity:
Gaps:
Outliers:
Symmetric about 4
One peak at 4
Not Skewed
Not Uniform
No Gaps
Take it further!
No Outliers
(1.5 - min) 41 – 42.5
In-Class Notes
If you don’t want to display the answers, click “next slide” at the bottom.
Problems 1 and 4 have some extra parts for any students who are up to the challenge. Hit the “Take it further” button to show prompt.
Hit the Fun Fact Button to display the name for this type of graph (normal distribution)
Preparation Notes
Try not to spend too long of a time on these questions, because they can get drawn out. Rather, try and find a fluid, standard way to move
through each exercise with your students, so they can get used to the standard practice.
Can you calculate a center for this graph?
Can you calculate a spread for this graph?
Graphs that are symmetric with one peak are also called “normal distributions” since they are the most common.
Fun Fact!
Agenda

14. Practice Describe the SHAPE of this graph: Symmetry: Peaks:
Skewness:
Uniformity:
Gaps:
Outliers:
Symmetric about 3.5
(Disregard the outlier)
No Peak
Not Skewed
Uniform
Gap at 7
(1.5- min)
In-Class Notes
If you don’t want to display the answers, click “next slide” at the bottom.
Problems 1 and 4 have some extra parts for any students who are up to the challenge. Hit the “Take it further” button to show prompt.
Preparation Notes
Try not to spend too long of a time on these questions, because they can get drawn out. Rather, try and find a fluid, standard way to move
through each exercise with your students, so they can get used to the standard practice.
Outlier at 8
Agenda

15. Practice Describe the SHAPE of this graph: Symmetry: Peaks:
Skewness:
Uniformity:
Gaps:
Outliers:
Not Symmetric
Two Peaks at 2 and 6
Not Skewed
Not Uniform
One Gap at 4
(1.5 - min)
In-Class Notes
If you don’t want to display the answers, click “next slide” at the bottom.
Problems 1 and 4 have some extra parts for any students who are up to the challenge. Hit the “Take it further” button to show prompt.
Preparation Notes
Try not to spend too long of a time on these questions, because they can get drawn out. Rather, try and find a fluid, standard way to move
through each exercise with your students, so they can get used to the standard practice.
No Outliers
Agenda

16. Practice Describe the SHAPE of this graph: Symmetry: Peaks: Skewness:
Uniformity:
Gaps:
Outliers:
Not Symmetric
One peak at 1
Skewed right
Not Uniform
No Gaps
Take it further!
(1.5 - min)
In-Class Notes
If you don’t want to display the answers, click “next slide” at the bottom.
Problems 1 and 4 have some extra parts for any students who are up to the challenge. Hit the “Take it further” button to show prompt.
Preparation Notes
Try not to spend too long of a time on these questions, because they can get drawn out. Rather, try and find a fluid, standard way to move
through each exercise with your students, so they can get used to the standard practice.
No Outliers
Can you calculate a center for this graph?
Can you calculate a spread for this graph?
Agenda