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Session 5 of 8
Understanding Averages
Mean, median, mode, range — four tools that each tell a different part of the data's story.
📊 Data Science for Young Minds · Grade 4
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Opening Hook
Which Number Best Describes This Group?
If someone asked you "what's a typical number here?" — what would you say?
Today we'll learn 4 different ways to answer that question — and discover that each one tells a slightly different story.
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Today's Plan
What We're Doing Today
- ➕ Mean — add all, divide by count
- 🎯 Median — find the middle value
- 🔁 Mode — find the most frequent value
- 📏 Range — max minus min
- 🤔 When is each measure most useful?
- 🎮 Calculate all 4 for our dataset — then compare!
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Lesson 1
The Mean — Step by Step
The mean is what most people call "the average." Here's how to find it:
Step 1 — Add all values
4 + 7 + 3 + 9 + 7 + 5 + 7 = ?
= 42
Step 2 — Count how many values
4, 7, 3, 9, 7, 5, 7 → count them → 7 values
Step 3 — Divide the sum by the count
42 ÷ 7 =
Mean = 6
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Lesson 2
The Median — Find the Middle
The median is the middle value when data is ordered from least to greatest.
Step 1 — Order the values
3, 4, 5, 7, 7, 7, 9
Step 2 — Find the middle (remove from each end)
~~3~~ ~~4~~ ~~5~~ 7 ~~7~~ ~~7~~ ~~9~~ → one card left!
Median = 7
💡 With 7 values, the median is always the 4th value when ordered.
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Lesson 3
The Mode — Most Frequent
The mode is the value that appears most often in the dataset.
7 appears 3 times — more than any other value.
Mode = 7
A dataset can have no mode (all different), one mode, or multiple modes.
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Lesson 4
The Range — Measuring Spread
The range tells us how spread out the data is.
Formula
Range = Maximum − Minimum
Our Dataset: 3, 4, 5, 7, 7, 7, 9
Maximum = 9 · Minimum = 3
Range = 9 − 3 = 6
A range of 6 means the values span 6 units. A large range = data is spread out. A small range = data is tightly clustered.
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All Four Together
Our Complete Picture
Dataset: 4, 7, 3, 9, 7, 5, 7
➕ Mean
Add all ÷ count
42 ÷ 7
= 6
🔁 Mode
Most frequent
7 appears 3 times
= 7
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Activity!
Calculate All Four — Your Turn
Use the same dataset: 4, 7, 3, 9, 7, 5, 7
- 📝 Show your work for each calculation on your worksheet
- 🃏 Use your number cards to find the median physically
- 📊 Fill in the comparison table on your worksheet
- 💬 Write: which measure best describes this data, and why?
⏱ 15 minutes — refer to the worked example on the board if needed!
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🧠
Brain Break — Mental Mean!
Three quiz scores: 8, 6, 10. What is the mean?
Add them up, divide by 3. No pencil!
Now try: 5, 7, 9. Mean? Now: 4, 8, 6. Mean?
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Big Discussion
Which Measure Tells the Best Story?
"If you were a teacher looking at test scores — would you use mean, median, or mode to describe how the class did? What about a student hoping to argue their grade was unfair?"
- 🏫 Real estate agents use median for house prices (one mansion skews the mean)
- 👟 Shoe stores order by mode (most popular size sells most)
- 📝 Report card averages use mean (balances all grades)
- 🌡️ Weather reports give range (high of 85, low of 60)
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When to Use Each
Choosing the Right Measure
Use Mean When…
- Data is balanced (no extreme outliers)
- You want to account for every value equally
- Example: class test average
Use Median When…
- One extreme value might distort the mean
- Example: house prices, salaries
- The "middle person" is more typical
Use Mode When…
- You want the most popular choice
- Data is categorical (favorite color)
- Example: most common shoe size
Use Range When…
- Describing spread/variability
- Comparing consistency of two groups
- Example: temperature variation
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The Outlier Effect
What Happens With an Extreme Value?
Add one extreme value to our dataset: 4, 7, 3, 9, 7, 5, 7, 50
Before (without 50)
- Mean = 6
- Median = 7
- Mode = 7
After (with 50)
- Mean = 92 ÷ 8 = 11.5 ↑↑
- Median = (7+7)÷2 = 7 (barely changed)
- Mode = 7 (unchanged)
One extreme value can dramatically change the mean while barely affecting the median. This is why context always matters!
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Vocabulary Review
Words to Know
Mean
Sum of all values ÷ number of values
Median
Middle value when data is ordered least to greatest
Mode
Value that appears most often in the dataset
Range
Maximum value minus minimum value
Typical value
A number representing what is "normal" in the data
Outlier
A value far away from the rest of the data
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Wrap Up
Session 5 Complete!
- ✅ Mean = sum ÷ count — sensitive to extreme values
- ✅ Median = middle value — resistant to extreme values
- ✅ Mode = most frequent — works for categorical data too
- ✅ Range = spread of data — not a measure of center
- ✅ Choosing the right measure depends on the data's story
🔮 Coming up — Session 6: Data that changes over time — line graphs, trends, and making predictions!