Central Tendency Mean Median Mode

Who this is for

• Aspiring and junior Data Analysts who summarize datasets for reports and dashboards.
• Professionals switching into analytics who need a reliable way to describe "typical" values.
• Students preparing for analytics interviews or case studies.

Prerequisites

• Basic arithmetic (sum, division) and comfort with sorting numbers.
• Familiarity with data types: numeric vs categorical.
• Optional: Knowing spreadsheet basics (e.g., functions like AVERAGE, MEDIAN, MODE) helps but is not required.

Why this matters

Central tendency helps you answer: "What is typical here?" Data Analysts use it to:

• Summarize monthly revenue or daily active users in executive dashboards.
• Choose a fair price or "typical" delivery time shown to customers.
• Detect when outliers are skewing reports (e.g., one huge order distorting averages).
• Compare performance across versions, branches, or time periods quickly.

Concept explained simply

Mean (average)

Add up all values and divide by how many values there are. Mental model: a balance point — if the data were weights on a line, the mean is where the seesaw balances.

Formula: mean = (sum of values) / (count of values).

Median (middle)

Order the values. The median is the middle one. If there are two middle values (even count), take their average. Mental model: a robust midpoint that ignores how big the extremes are.

Mode (most frequent)

The value that appears most often. Works for numbers and categories. Mental model: the peak of the distribution — the most common choice.

Mental model

• Mean: pulled by outliers like a magnet; one extreme value can move it a lot.
• Median: stands firm in the middle; resistant to extremes.
• Mode: reflects the crowd’s favorite; may be multiple favorites.

Worked examples

Example 1: Clean numeric data

Data: [2, 3, 5, 5, 9]

Example 2: Skew due to an outlier

Monthly incomes (k): [40, 45, 50, 50, 55, 60, 60, 62, 65, 200]

Example 3: Categorical data (mode only)

Favorite color survey: [Red, Blue, Blue, Green, Blue, Red]

Example 4: Weighted mean (ratings)

Ratings counts: 5★: 120, 4★: 60, 3★: 15, 2★: 5, 1★: 0

How to compute quickly

1. Check data type and quality: numeric vs categorical; handle missing values; note outliers.
2. For mean: sum values; divide by count. For weighted mean: multiply each value by its weight, sum results, divide by total weight.
3. For median: sort values; pick middle (or average the two middles).
4. For mode: count frequencies; pick the highest. Multiple modes are possible.

Exercises

These mirror the exercises section below. Try them now; then expand the solutions.

Self-check checklist

• I sorted data before computing the median.
• I verified whether outliers are present and decided accordingly (mean vs median).
• For weighted averages, I divided by total weight (not count of categories).
• I reported the sample size (n) when sharing results.

Common mistakes and how to self-check

• Mistake: Using the mean on heavily skewed data. Fix: Inspect distribution; prefer median.
• Mistake: Forgetting to sort before taking the median. Fix: Always sort first.
• Mistake: Dividing weighted sums by the number of groups. Fix: Divide by total weight.
• Mistake: Reporting mode for continuous data with no repeats. Fix: State "no clear mode" or bin sensibly.
• Mistake: Not handling missing values consistently. Fix: Exclude missing from both sum and count; report n.

Practical projects

• Support analytics: Determine the typical resolution time across tickets; compare mean vs median and explain the difference.
• E-commerce: Compute median order value by traffic source; flag sources with strong skew.
• App ratings: Build a simple report that shows mode rating and weighted average rating over time.
• Logistics: Compare median delivery time before and after a route change; quantify the percent change.

Mini challenge

You have delivery times (minutes): [18, 19, 20, 21, 22, 120]. Your manager asks for a single typical value for the homepage. Which measure do you use and what value do you report?

Learning path

1. Master central tendency (this lesson): compute mean, median, mode; choose the right one based on data shape.
2. Then learn variability: range, IQR, variance, standard deviation — they give context to the typical value.
3. Move to distributions and skewness/kurtosis to better choose summary measures.
4. Apply in dashboards: include both typical value and variability to avoid misleading summaries.

Next steps

• Take the Quick Test below to lock in the concepts. Test is available to everyone; only logged-in users will have progress saved.
• Apply to a small dataset you own (sales, usage, or survey). Report mean vs median and explain differences in one paragraph.