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Basic Statistics · Mean, Median, and Standard Deviation

Basic Statistics (Mean, Median, Standard Deviation)

📂IT · Data · DX⏱2-min read📊Beginner🔗6 related

What are basic statistics?

In one line
The basic tools for summarizing a data set in a few numbers. The mean and median show where the center is, and the standard deviation shows how widely the values are spread around that center.
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⚡ Summary in 3 lines
  • An average alone doesn’t show how a course really went
  • Read a measure of the center together with a measure of spread
  • An average without a respondent count and response rate is not a basis for decisions

A training results report always includes "average satisfaction of 4.3." But a single mean cannot tell you how the course actually went. A course where everyone gave a 4 and a course where half gave a 5 and some gave a 1 can produce the same mean. In practice, basic statistics is less about calculation than about what to look at alongside the mean. The starting point is to read one value for the center and one value for the spread as a pair.

The mean is the sum of all values divided by their count, so a single extreme value can pull it a long way. The median is the middle value when the data is sorted by size, so extreme values affect it less. For data with a few large values mixed in, such as salaries or training costs, the median is closer to the real picture. A big gap between the two signals a skewed distribution, and reporting only the mean will mislead the reader.

The standard deviation is found by squaring each value's distance from the mean, averaging those squares, and taking the square root. On a 5-point scale, you can read a standard deviation of around 0.5 as opinions clustered together, and above 1 as opinions divided. In Excel, use AVERAGE for the mean and MEDIAN for the median. For the standard deviation, use STDEV.S when respondents are a sample of the whole group and STDEV.P when everyone responded. Plot the number of respondents per score as a bar chart next to the figures, and what the standard deviation is telling you becomes clear at a glance.

In practice, the common mistake is reading meaning into small differences. With 12 respondents, averages of 4.4 and 4.2 can flip if one person changes a score, yet instructors get ranked and contracts renewed on that gap. It is also common to report the average of a survey with a 40% response rate as if it reflected everyone’s opinion. Even the average of a 5-point scale is a summary that assumes equal intervals between points. A report should show the number of respondents, the response rate, and the share scoring 4 or higher next to the average, so readers can judge how far to trust the number.

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💡 In plain English
It is like soaking one foot in ice water and the other in hot water, and being told the average temperature is lukewarm.
Why it matters in practice
When you compile satisfaction and assessment scores for the year-end training results report, two questions come up: whether the mean alone is enough, and how to explain differences between courses.
🧮 Formula
Mean = sum of values ÷ count / Median = the middle value when sorted from smallest to largest / Sample standard deviation = √( Σ(each value − mean)² ÷ (count − 1) )
If satisfaction responses are 5, 5, 4, 4, and 2, the mean is 20 ÷ 5 = 4.0 and the median is 4. The sum of squared deviations is 1 + 1 + 0 + 0 + 4 = 6, and the square root of 6 ÷ (5 − 1) = 1.5, about 1.22, is the sample standard deviation.
Origin and sources

Mean, median, and standard deviation are the basic tools of descriptive statistics for summarizing data. They were formalized one after another as statistics developed, and today they are built-in spreadsheet functions. Rather than tracing founders or dates, this page focuses on how to read them together in practice.

An example

Consider a hypothetical case. The training team at Company A, a chemical company with 450 employees, ran a leadership course and a problem-solving course in the second half of the year, with 40 participants each. The average satisfaction on a 5-point scale was 4.1 for both, and the draft results report said, "Both courses performed well."

  1. A training team associate calculated the medians: 5 for the leadership course and 4 for the problem-solving course. The team lead said, “The averages are the same, but the medians differ. Let’s look at the distribution.”
  2. Counting responses at each score, the leadership course had 26 people at 5 points, 6 at 4 points, 2 at 2 points, and 6 at 1 point. The problem-solving course had 8 people at 5 points, 28 at 4 points, and 4 at 3 points.
  3. The standard deviation was about 1.5 for the leadership course and about 0.5 for the problem-solving course. The assistant manager summed it up: "One course had split opinions, and the other was consistently fine."
  4. Reading the open-ended answers from the 6 people who gave a 1, the team found that all had been promoted three or more years earlier, and all wrote "a repeat of what I already know." The cause was how participants were selected.
  5. The team lead changed the report template to show the median, standard deviation, number of respondents, and share of scores of 4 or higher next to the mean. The leadership course had 80% scoring 4 or higher.
  6. In the next cohort, the leadership course was split into two classes by years of experience. Scores of 1 dropped from 6 respondents to 0, and the standard deviation fell from 1.5 to 0.6.
Related terms
Satisfaction Survey Design · Reaction EvaluationA survey that measures learners’ reactions right after training. Depending on how the questions are designed, it can produce information you can act on or leave you with a score that means little.Data LiteracyThe ability to read, interpret, and use data, and to communicate with it. It is a basic skill for all employees, and its core is not statistical expertise but the habit of asking the right questions and doubting the numbers.Kirkpatrick Four-Level EvaluationThe classic training evaluation model that assesses effectiveness at four levels: reaction, learning, behavior, and results.Learning AnalyticsA data-driven approach that collects and analyzes learning data (completion, participation, achievement, behavior) to assess and improve training effectiveness.Pivot Table · Spreadsheet Data AnalysisA spreadsheet feature that summarizes row-level raw data with simple drag-and-drop, instantly producing totals and comparisons by category.Correlation vs. CausationCorrelation means two values move together; causation means one causes the other. Moving together alone does not show cause and effect.
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Last updated 14 Oct 2026 · Reviewed by John Kim

FAQ

It’s best to report both. If the two values are close, the mean alone is enough. If they differ widely, a few extreme values are pulling the mean, so show the median and the distribution as well to avoid misleading readers.
There is no absolute threshold; it depends on the scale and context. For satisfaction on a 5-point scale, around 0.5 is commonly read as opinions clustered and above 1 as opinions divided. The most practical approach is to compare against your organization's past courses.
Use STDEV.S when your data is a sample, a subset of the whole, because it divides by the count minus 1. Use STDEV.P when your data covers the entire population, because it divides by the count itself. If only some participants answered a survey, STDEV.S is the right choice.
With only 10 to 20 respondents, one or two answers can move the mean sharply. Don't rank courses or instructors on a difference of a single decimal place. Always report the number of respondents and the response rate alongside the score, so the limits of the figure are visible.