Thinkabara

📈 Intro to Statistics · Lesson 2 of 7

Mean, median and mode

Google Classroom

Measures of center, and which one to use when data are skewed.

Three centers

MeanAdd the values and divide by how many: x̄ = Σx / n
MedianThe middle value when sorted (average of the two middle ones if n is even)
ModeThe most common value — useful for categories

Worked example

Weekly hours of part-time work for 7 students: 0, 5, 8, 10, 12, 15, 40. Mean = 90 ÷ 7 ≈ 12.9 hours. Median = 10 (the 4th of 7 values). The one student working 40 hours pulls the mean up; the median isn’t affected.

Shape and choice

SymmetricMean ≈ median — either works; report the mean
Right-skewed (long tail to the right)Mean > median — report the median (incomes, home prices)
Left-skewedMean < median
OutliersPull the mean, not the median

In a spreadsheet

=AVERAGE(B2:B8)   → mean
=MEDIAN(B2:B8)    → median
=MODE(B2:B8)      → mode

Works the same in Excel and Google Sheets.

Tip

💡 When a news story says “the average American…”, ask whether it’s the mean or the median — for income, the difference is large.

✏️ Practice: your turn

  1. Find the mean and median of your last 7 days of sleep
  2. Add an outlier (e.g., 14 hours) and recompute — which changed more?
  3. Decide which center to report for US household income and why
  4. Check your answers with the calculator’s Statistics tab

✏️ Scientific calculator with a statistics tab (mean, median, standard deviation)

🧠 Quick quiz

Answer all 4 questions correctly to mark this lesson as done.

1. Median of 2, 4, 9, 11, 30?
2. Mean of 2, 4, 9, 11, 30?
3. Which is resistant to outliers?
4. In right-skewed data…

0 of 4 correct

All lessons in Intro to Statistics

  1. 🎲 1. Data, variables and samplingCategorical vs. quantitative, populations, samples and bias
  2. 🎯 2. Mean, median and modeMeasures of center, and which one to use when data are skewed
  3. ↔️ 3. Spread: range, IQR and standard deviationHow spread out the data are, and how to read a box plot
  4. 🔔 4. The normal curve and z-scoresThe 68–95–99.7 rule and comparing values on different scales
  5. 📉 5. Correlation and regressionScatterplots, r, the line of best fit — and causation
  6. 🎯 6. Confidence intervalsEstimate ± margin of error, and what “95% confident” means
  7. ⚗️ 7. Hypothesis tests and p-valuesNull and alternative, the p-value, significance and errors