Lesson Plan
Measure Up!
Students will be able to summarize numerical data sets, including providing quantitative measures of center (mean, median) and variability (interquartile range, mean absolute deviation).
Understanding how to summarize data helps us make sense of information all around us, from sports statistics to survey results, empowering you to make informed decisions.
Audience
7th Grade Stud6thents
Time
30 minutes
Approach
Direct instruction, guided practice, and independent application.
Materials
Whiteboard or Projector, Markers or Pens, Slide Deck: Measure Up!, Worksheet: Data Deep Dive, and Answer Key: Data Deep Dive
Prep
Teacher Preparation
10 minutes
- Review the Slide Deck: Measure Up! content and teacher notes.
- Print copies of the Worksheet: Data Deep Dive for each student.
- Have the Answer Key: Data Deep Dive ready for quick reference.
- Ensure whiteboard or projector is set up and ready to use.
- Gather markers or pens for demonstration.
Step 1
Introduction: What's the Story in the Data?
5 minutes
- Begin with a hook question: "Imagine you have a big pile of numbers. How would you tell someone what those numbers are all about without listing every single one?"
- Introduce the lesson objective: Today, we're going to learn how to tell the 'story' of a data set using just a few important numbers: measures of center and measures of variability.
- Display the first few slides of Slide Deck: Measure Up! to set the stage and introduce key vocabulary (mean, median, interquartile range, mean absolute deviation).
Step 2
Direct Instruction: Center and Variability Explained
10 minutes
- Use Slide Deck: Measure Up! to explain and demonstrate how to calculate:
- Measures of Center: Mean (average) and Median (middle value).
- Measures of Variability: Interquartile Range (IQR) and Mean Absolute Deviation (MAD).
- Provide clear, step-by-step examples for each calculation. Encourage students to ask questions.
- Emphasize the 'why' behind each measure – what does it tell us about the data?
Step 3
Guided Practice: Let's Crunch Some Numbers!
8 minutes
- Distribute the Worksheet: Data Deep Dive.
- Work through the first problem on the worksheet together as a class. Guide students through calculating the mean, median, IQR, and MAD for a small data set.
- Circulate around the room, offering support and checking for understanding as students begin working on the second problem independently or in pairs.
Step 4
Independent Application & Wrap-up
7 minutes
- Students continue working on the Worksheet: Data Deep Dive.
- Review answers to the guided practice problem using the Answer Key: Data Deep Dive and address any common misconceptions.
- Assign any unfinished problems on the worksheet as homework or for further practice.
- Conclude by reiterating the importance of summarizing data effectively: "Now you have the tools to tell the full story of any data set!"
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Slide Deck
What's the Story in the Numbers?
Imagine you have a big pile of numbers...
How would you tell someone what those numbers are all about without listing every single one?
Today, we'll learn how to summarize data to tell its story!
Greet students and introduce the topic with an engaging question to activate prior knowledge and set the stage for understanding data summaries.
Our Goal Today:
By the end of this lesson, you will be able to:
* Summarize numerical data sets.
* Provide quantitative measures of center (mean, median).
* Provide quantitative measures of variability (interquartile range, mean absolute deviation).
Explain the objective clearly. Students should know what they are expected to learn by the end of the lesson.
Measures of Center: Where's the Middle?
Measures of Center tell us about the 'typical' or 'middle' value in a data set.
1. Mean (The Average):
* Add all the numbers together.
* Divide by how many numbers there are.
* Example: Data: 2, 4, 6
* Sum = 12, Count = 3, Mean = 12 / 3 = 4
Introduce measures of center. Start with mean, as it's often the most familiar. Provide a simple example.
Measures of Center: Where's the Middle?
2. Median (The Middle Number):
* Order the numbers from least to greatest.
* Find the middle number.
* If there are two middle numbers, find their average.
* Example (Odd): Data: 1, 3, 7, 9, 10
* Median = 7
* Example (Even): Data: 2, 4, 6, 8
* Middle numbers are 4 and 6, Median = (4+6)/2 = 5
Explain the median. Emphasize ordering the data first and how to handle even vs. odd numbers of data points.
Measures of Variability: How Spread Out Is It?
Measures of Variability tell us how 'spread out' or 'scattered' our data is.
1. Interquartile Range (IQR):
* It's the range of the middle 50% of your data.
* Step 1: Order the data and find the Median (Q2).
* Step 2: Find the median of the lower half (Q1).
* Step 3: Find the median of the upper half (Q3).
* Step 4: IQR = Q3 - Q1
Transition to measures of variability. Explain that center isn't enough; we need to know how spread out the data is. Introduce IQR.
IQR Example
Data: 1, 3, 5, 7, 9, 11, 13, 15
1. Order data (already done!).
2. Median (Q2) = (7+9)/2 = 8
3. Lower Half: 1, 3, 5, 7. Q1 = (3+5)/2 = 4
4. Upper Half: 9, 11, 13, 15. Q3 = (11+13)/2 = 12
5. IQR = Q3 - Q1 = 12 - 4 = 8
Provide a clear example for calculating IQR.
Measures of Variability: How Spread Out Is It?
2. Mean Absolute Deviation (MAD):
* It's the average distance of each data point from the mean.
* Step 1: Calculate the Mean of the data set.
* Step 2: Find the absolute difference between each data point and the Mean.
* Step 3: Sum all those absolute differences.
* Step 4: Divide the sum by the number of data points.
Introduce Mean Absolute Deviation (MAD). Explain its purpose and the steps involved. This can be more complex, so take it slowly.
MAD Example
Data: 2, 4, 6, 8
1. Mean = (2+4+6+8)/4 = 20/4 = 5
2. Absolute Differences from Mean (5):
* |2 - 5| = 3
* |4 - 5| = 1
* |6 - 5| = 1
* |8 - 5| = 3
3. Sum of Differences = 3 + 1 + 1 + 3 = 8
4. MAD = 8 / 4 = 2
Provide an example for MAD, breaking it down into steps.
Time to Practice!
Now it's your turn to be data detectives!
* Work on the Worksheet: Data Deep Dive.
* We'll start with the first problem together, then you can tackle the rest.
* Don't be afraid to ask questions!
Instruct students to work on the worksheet, starting with the guided practice problem. Encourage collaboration and questions.
You've Got the Power of Data!
You now have powerful tools to:
* Calculate measures of center (mean, median).
* Calculate measures of variability (IQR, MAD).
* Tell the story of data effectively!
Keep exploring and making sense of the numbers around you!
Final slide to wrap up the lesson, emphasizing the importance of what they learned.
Worksheet
Data Deep Dive: Summarizing Numerical Data
Name: ____________________________
Instructions: For each data set, calculate the mean, median, interquartile range (IQR), and mean absolute deviation (MAD). Show your work!
Problem 1: Basketball Scores
The points scored by a basketball team in their last 8 games are:
12, 15, 10, 18, 20, 13, 15, 17
-
Order the data from least to greatest:
-
Mean:
-
Median (Q2):
-
Interquartile Range (IQR):
- Q1:
- Q3:
- IQR = Q3 - Q1:
- Q1:
-
Mean Absolute Deviation (MAD):
- Absolute Differences from the Mean:
- Sum of Absolute Differences:
- MAD:
- Absolute Differences from the Mean:
Problem 2: Plant Growth (in cm)
A scientist measured the growth of 7 plants over a month:
2.5, 3.0, 2.0, 3.5, 4.0, 2.5, 3.0
-
Order the data from least to greatest:
-
Mean:
-
Median (Q2):
-
Interquartile Range (IQR):
- Q1:
- Q3:
- IQR = Q3 - Q1:
- Q1:
-
Mean Absolute Deviation (MAD):
- Absolute Differences from the Mean:
- Sum of Absolute Differences:
- MAD:
- Absolute Differences from the Mean:
Answer Key
Data Deep Dive: Summarizing Numerical Data - Answer Key
Problem 1: Basketball Scores
The points scored by a basketball team in their last 8 games are:
12, 15, 10, 18, 20, 13, 15, 17
-
Order the data from least to greatest:
10, 12, 13, 15, 15, 17, 18, 20 -
Mean:
- Sum = 10 + 12 + 13 + 15 + 15 + 17 + 18 + 20 = 120
- Count = 8
- Mean = 120 / 8 = 15
-
Median (Q2):
- Ordered data: 10, 12, 13, 15, 15, 17, 18, 20
- The two middle numbers are 15 and 15.
- Median = (15 + 15) / 2 = 15
-
Interquartile Range (IQR):
- Lower half: 10, 12, 13, 15
- Q1 (median of lower half) = (12 + 13) / 2 = 12.5
- Upper half: 15, 17, 18, 20
- Q3 (median of upper half) = (17 + 18) / 2 = 17.5
- IQR = Q3 - Q1 = 17.5 - 12.5 = 5
-
Mean Absolute Deviation (MAD):
- Mean = 15
- Absolute Differences from the Mean:
- |10 - 15| = 5
- |12 - 15| = 3
- |13 - 15| = 2
- |15 - 15| = 0
- |15 - 15| = 0
- |17 - 15| = 2
- |18 - 15| = 3
- |20 - 15| = 5
- Sum of Absolute Differences = 5 + 3 + 2 + 0 + 0 + 2 + 3 + 5 = 20
- MAD = 20 / 8 = 2.5
Problem 2: Plant Growth (in cm)
A scientist measured the growth of 7 plants over a month:
2.5, 3.0, 2.0, 3.5, 4.0, 2.5, 3.0
-
Order the data from least to greatest:
2.0, 2.5, 2.5, 3.0, 3.0, 3.5, 4.0 -
Mean:
- Sum = 2.0 + 2.5 + 2.5 + 3.0 + 3.0 + 3.5 + 4.0 = 20.5
- Count = 7
- Mean = 20.5 / 7 \approx 2.93 (rounded to two decimal places)
-
Median (Q2):
- Ordered data: 2.0, 2.5, 2.5, 3.0, 3.0, 3.5, 4.0
- Median = 3.0
-
Interquartile Range (IQR):
- Lower half: 2.0, 2.5, 2.5
- Q1 (median of lower half) = 2.5
- Upper half: 3.0, 3.5, 4.0
- Q3 (median of upper half) = 3.5
- IQR = Q3 - Q1 = 3.5 - 2.5 = 1.0
-
Mean Absolute Deviation (MAD):
- Mean \approx 2.93
- Absolute Differences from the Mean (rounded to two decimal places):
- |2.0 - 2.93| = 0.93
- |2.5 - 2.93| = 0.43
- |2.5 - 2.93| = 0.43
- |3.0 - 2.93| = 0.07
- |3.0 - 2.93| = 0.07
- |3.5 - 2.93| = 0.57
- |4.0 - 2.93| = 1.07
- Sum of Absolute Differences = 0.93 + 0.43 + 0.43 + 0.07 + 0.07 + 0.57 + 1.07 = 3.57
- MAD = 3.57 / 7 \approx 0.51 (rounded to two decimal places)