A balanced beam with data blocks settling at their balance point, an infographic about measures of center.
Statistics · 6.SP

Lesson 6.2 — Mean, Median & Mode

Three different ways to find the "center" of a pile of numbers — and they don't always agree.

🎙️ Narration script

Welcome back! Today we're learning three different ways to find the center of a group of numbers: the mean, the median, and the mode. And here's the fun part, they don't always agree.

When you have a list of numbers, you often want just one number that describes the whole group. That's called a measure of center.

First, the mean. That's the average. You add up all the values, then divide by how many there are. Think of it as the balancing point of your data.

Next, the median. That's the middle value once you've put the numbers in order. And here's an important reminder: for the median, you have to sort first. If there's an even number of values, you take the two in the middle and average them.

Third, the mode. That's just the value that shows up most often. A set can have one mode, more than one, or sometimes none at all.

Let's work an example with the numbers three, five, five, seven, and ten. For the mean, add them up: three plus five plus five plus seven plus ten is thirty. Divide by five values, and you get six. For the median, they're already in order, and the middle one is five. For the mode, five appears twice, so the mode is five.

Now, why are the mean and median sometimes different? Because of outliers. An outlier is a value way out from the rest. It pulls the mean toward it, but it barely moves the median. That's why news reports use the median house price, so one giant mansion doesn't throw off the whole number.

Quick recap. Mean: add and divide. Median: the middle of the sorted list. Mode: the most frequent value. And watch out for those outliers!

1 Core idea

When you have a list of numbers, you often want one number that describes the whole group. That single number is a measure of center. There are three common ones: the mean (the balancing-point average), the median (the middle value when sorted), and the mode (the value that shows up most). They answer slightly different questions, so it helps to know all three.

🧩 Think of it like… the mean is the balance point of a seesaw — if every data value were a weight placed on a number-line plank, the mean is the single spot where the plank would tip level. For 3, 5, 5, 7, 10 that balance point lands at 6.
Where it breaks: the balance point need not be an actual data value or even a whole number — 6 is the mean of 3, 5, 5, 7, 10, but nobody in that set scored a 6. The median, by contrast, is always a real "middle person."

2 Key terms

Mean (average)
Add all the values, then divide by how many there are.
Median
Put the values in order; the median is the middle one. With an even count, average the two middle values.
Mode
The value that appears most often. A set can have one mode, several, or none.
Data set
The whole collection of numbers you are studying.
Outlier
A value far away from the rest — it can pull the mean up or down a lot.

3 Real-life examples

  • Test scores: your average grade is the mean of your scores.
  • House prices: news reports use the median price so one giant mansion doesn't skew it.
  • Shoe store: the most-sold size is the mode — that's what they restock most.
  • Quiz set 3, 5, 5, 7, 10: mean = 6, median = 5, mode = 5.
🤔 Pause & think: Why does a single huge outlier drag the mean far but barely budge the median?
Reveal the thinking
The mean adds up every value, so a giant number inflates the total and pulls the average toward it. The median only cares about position in the sorted list — an extreme value just sits at the far end and shoves the middle over by one slot at most. Add a 20 to 3, 5, 5, 7, 10: the median creeps from 5 to 6, but the mean leaps from 6 to 50 ÷ 6 ≈ 8.3.

4 Common doubts

Do I sort the numbers before finding the mean?

No — for the mean, order doesn't matter; you just add and divide. Sorting only matters for the median.

What if two numbers tie for "most often"?

Then the set has two modes (it's "bimodal"). If every value appears the same number of times, there is no mode.

Why are mean and median sometimes different?

An outlier pulls the mean toward it but barely moves the median. That's why median is "fairer" for skewed data like prices or incomes.

How do I find the median of an even-sized list?

Sort it, find the two middle values, and take their mean. For 2, 4, 6, 8 → middle pair is 4 and 6 → median = 5.

5 Step-by-step (all three for 3, 5, 5, 7, 10)

  1. Mean: add them: 3 + 5 + 5 + 7 + 10 = 30. Divide by 5 values: 30 ÷ 5 = 6.
  2. Median: already sorted; 5 values, so the middle (3rd) one is 5.
  3. Mode: 5 appears twice, everything else once, so the mode is 5.

📊 See it · the mean is the balance point

Dot plot of 3, 5, 5, 7, 10. The triangle (▲) marks the mean = 6 — the spot where the dots would balance like weights on a seesaw.

0 2 3 5 6 7 10 12 mean = 6

Now the numbers:

3 + 5 + 5 + 7 + 10 = 30 → add all 5 values
mean = 30 ÷ 5 = 6 → divide by the count
median = 3, 5, 5, 7, 10 → middle value
mode = 5 → appears most often (twice)
✅ Check yourself
  1. Find the median of 2, 4, 6, 8.
    answer Even count, so average the two middle values: (4 + 6) ÷ 2 = 5.
  2. For 2, 3, 10, is the mean bigger or smaller than the median, and why?
    answer Mean = 15 ÷ 3 = 5; median = 3. The mean is bigger because the outlier 10 inflates the total and pulls the average up, while the median stays anchored at the middle value.
⚡ Quick recap. The mean adds everything and divides by the count (balance point); the median is the middle of the sorted list; the mode is the most frequent value. For 3, 5, 5, 7, 10 → mean 6, median 5, mode 5. Watch for outliers — they move the mean, not the median.

Grounded in CA CCSS-M, Grade 6 · 6.SP (summarizing data with measures of center), California Department of Education. Hero image generated with Gemini Nano Banana Pro.