Statistics: Mean, Median, Mode
When you have a bunch of numbers — test scores, home prices, ages of everyone in a movie theater — it's often useful to describe them with a single number. Statisticians call that a "measure of center." The three most common are the mean, the median, and the mode. They usually give different answers, and choosing the right one matters.
The three measures
**Mean** (the average): add up all the numbers and divide by how many there are.\n\n**Median**: put the numbers in order. The median is the one in the middle. (If there are two middle numbers, average them.)\n\n**Mode**: the number that appears most often. A list can have no mode, one mode, or many modes.
Example: test scores 70, 75, 80, 80, 95.\n- Mean = (70 + 75 + 80 + 80 + 95) ÷ 5 = 400 ÷ 5 = **80**\n- Median = middle number = **80**\n- Mode = most common = **80**\n\nThey all agree here. But they don't always.
What is the median of 3, 7, 7, 10, 12?
When the choice matters: outliers
Imagine 5 people are in a room. Their incomes are $30K, $35K, $40K, $45K, and $50K.\n\n- Mean = $40K\n- Median = $40K\n\nNow Jeff Bezos walks in with his $200 billion.\n\n- Mean ≈ $33 billion (!!)\n- Median = $42.5K\n\nThe mean is useless now — it says "average" person in the room is a multi-billionaire, which is obviously wrong. The median shrugs off the outlier and tells you the truth: most people in the room make around $40K. This is why income statistics almost always use median, not mean.
For the data set 2, 3, 4, 5, 100, which measure of center best represents "typical"?
Mean vs. median in real data
Look up the median household income in your state (or country), and the mean household income. They'll be different. The mean will be higher. Write 2 sentences explaining why — based on what you just learned about outliers. This is the same math politicians and news articles sometimes exploit to make stats say what they want.
Variability: numbers aren't just their center
Two classes can have the same mean (say 80 on a test) but look totally different:\n- Class A: everyone scored 78, 79, 80, 81, 82 — tightly clustered.\n- Class B: some scored 50, others 100 — all over the place.\n\nTo describe variability at the grade 6 level, we use the **range** (max minus min) and the **interquartile range (IQR)** — the range of the middle half of the data. Both tell you "how spread out" the data is. CCSS 6.SP.5 asks you to report variability, not just center.
Collect your own data
Pick a question you can survey 10+ people about — how many hours of sleep they got last night, their favorite number under 100, the minutes they spend on homework. Collect the data. Then compute the mean, median, mode, and range. Write 2 sentences on what the center tells you, and 2 on what the variability tells you. If one number looks way off, decide: is it an outlier or real variation?
If a data set has no repeating values, what is the mode?
CCSS 6.SP emphasizes that statistics is about making sense of variability — understanding that data varies, and that summarizing it always loses information. Knowing when to use mean vs. median vs. mode, and reporting variability alongside center, is what separates honest statistics from misleading ones.
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