⚡ Grade 6 · Lesson 10 of 14
The Data Seesaw: Mean, Median, and Mode
Three different ways to name the 'typical' value in a data set — and why one outlier can tip the mean without budging the median.
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The big idea: Mean, median, and mode are three different ways to describe the 'center' of a data set. The mean is the balance point found by sharing the total evenly, the median is the middle value once the data is ordered, and the mode is the value that shows up most often — and they don't always agree, especially when an outlier is present.
Three ways to describe 'typical'
Imagine several friends' scores on a game sitting on a seesaw. If you wanted one number to describe the whole group, you have choices: the mean (the balance point), the median (the middle score once everyone lines up in order), and the mode (whichever score shows up most often). Each tells you something a little different about the data.
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Mean, median, and mode measure the center differently
The mean is the sum of all values divided by how many there are. The median is the middle value when the data is sorted from least to greatest. The mode is the value that appears most frequently — a data set can have one mode, more than one, or none at all.
\[ \text{mean} = \dfrac{\text{sum of all values}}{\text{number of values}} \]
The mean spreads the total evenly across every value — like leveling a seesaw.
Finding the median
To find the median, first put every value in order from least to greatest. If there is an odd number of values, the median is the single value exactly in the middle. If there is an even number of values, the median is the average of the two middle values.
🎮 Data Seesaw LIVE
Drag data points and watch the mean, median and mode respond. See how one outlier tips the mean.
Mode: the most popular value
The mode is simply the value that occurs most often in a data set. Unlike the mean and median, a data set can have no mode (if every value is different), one mode, or several modes (if two or more values tie for most frequent).
📝 Worked example: Find the mean, median, and mode of this data set: 4, 7, 4, 9, 6.
- Mean: add all values, 4 + 7 + 4 + 9 + 6 = 30, then divide by 5 values: 30 ÷ 5 = 6.
- Median: order the data — 4, 4, 6, 7, 9 — and take the middle (3rd) value: 6.
- Mode: 4 appears twice, more than any other value, so the mode is 4.
✓ Mean = <strong>6</strong>, median = <strong>6</strong>, mode = <strong>4</strong>.
📝 Worked example: Add one more score of 50 to the data set (now 4, 7, 4, 9, 6, 50). How do the mean and median change?
- New mean: sum = 4 + 7 + 4 + 9 + 6 + 50 = 80, divided by 6 values: 80 ÷ 6 ≈ 13.3.
- New median: order the data — 4, 4, 6, 7, 9, 50 — and average the two middle (3rd and 4th) values: (6 + 7) ÷ 2 = 6.5.
- The mean jumped from 6 to about 13.3, but the median barely moved, from 6 to 6.5.
✓ The <strong>mean</strong> is pulled sharply upward to about <strong>13.3</strong> by the outlier, while the <strong>median</strong> only shifts slightly, to <strong>6.5</strong>.
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Order the data before finding the median
The median is not just the middle number in the list as originally given — you must sort the values from least to greatest first. Skipping this step is the most common mistake.
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The median resists outliers better than the mean
Because the mean shares the total evenly, one unusually large or small value can drag it far from where most of the data sits. The median only cares about position in the order, so a single outlier barely moves it. When a data set has extreme values, the median often describes the “typical” case better than the mean.
Check your understanding
1. Find the mean of 3, 5, 7, 9, 6.
Sum = 3+5+7+9+6 = 30. Mean = 30 ÷ 5 = 6.
2. Find the median of 12, 3, 8, 15, 9.
Ordered: 3, 8, 9, 12, 15. The middle (3rd) value is 9.
3. What is the mode of 2, 4, 4, 6, 8, 4?
4 appears three times, more than any other value, so 4 is the mode.
4. Find the median of 10, 20, 30, 40 (an even number of values).
Ordered already: 10, 20, 30, 40. Average the two middle values: (20 + 30) ÷ 2 = 25.
5. A data set has one very large outlier. Which measure of center is affected the most?
The mean shares the total evenly across all values, so one extreme value pulls it strongly in that direction. The median, based on position, moves much less.
✅ Key takeaways
- The mean is the sum of all values divided by the number of values — the balance point of the data.
- The median is the middle value once the data is ordered from least to greatest (average the two middle values if there's an even count).
- The mode is the value that appears most often; a data set can have zero, one, or several modes.
- Always sort the data before finding the median.
- An outlier pulls the mean strongly toward it but barely shifts the median.