Mean, median, and mode

Mean, median and mode are the three measures of central tendency: three ways to describe the typical value in a set of numbers. The mean is the sum of the values divided by how many there are, the median is the middle value when they are sorted, and the mode is the value that appears most often. They are used to summarize data such as test scores, incomes, times or survey ratings, and they give different answers when the data is skewed or has outliers.

How to find the mean, median and mode

Take nine survey answers to "How many hours a week do you use the app?": 3, 7, 5, 9, 5, 4, 5, 8, 6.

Mean

Add all values and divide by the number of values.

3 + 7 + 5 + 9 + 5 + 4 + 5 + 8 + 6 = 52. Mean = 52 ÷ 9 = 5.78.

Median

Sort the values and take the middle one: 3, 4, 5, 5, 5, 6, 7, 8, 9. With 9 values the middle is the 5th, so the median = 5.

With an even number of values, the median is the average of the two middle ones. Add a tenth answer of 10: the sorted list is 3, 4, 5, 5, 5, 6, 7, 8, 9, 10, and the median = (5 + 6) ÷ 2 = 5.5. A median can therefore be a value nobody actually gave.

Mode

Count how often each value appears. 5 appears three times, more than any other value, so the mode = 5.

A dataset can have two modes (bimodal), several modes, or none, if every value appears once.

Which one to use

Survey rating scales sit in between. Single rating items are ordinal, so the median and the distribution are the safer summary. Means of rating scales are still widely reported, especially for multi-item scales and for comparing groups. If you report a mean, show the distribution or the median next to it.

What the gap between them tells you

• Mean ≈ median ≈ mode: the data is roughly symmetric with one peak.
• Mean above the median: a long tail of high values pulls the mean up (right skew). Typical for incomes and times.
• Mean below the median: a tail of low values pulls it down (left skew). Typical for satisfaction ratings, where most answers are high.

Survey example. 100 people rate a service from 1 to 5: 95 give 4 and 5 give 1. Mean = (95 × 4 + 5 × 1) ÷ 100 = 3.85. Median = 4, mode = 4. Reported alone, "average 3.85" sounds mediocre, although 95% of customers gave a 4. The median and the distribution tell the real story.

Second example. 5% give 1, 10% give 2, 15% give 3, 30% give 4 and 40% give 5. Mean = 3.9, median = 4, mode = 5. All three are informative: the typical customer is satisfied, and "5" is the most common answer.

Common mistakes

• Calculating a mean for categories. The average of region codes 1, 2 and 3 means nothing.
• Reading the mean as "what most people answered". A mean of 3 can come from everyone answering 3, or from half answering 1 and half answering 5.
• Using the mean for skewed data, such as income or completion time, where a few large values distort it.
• Reporting a center without spread. Add the standard deviation or the interquartile range, and the number of answers.
• Looking for a mode in continuous data without grouping it into intervals first, when every value may be unique.

How to calculate them for survey data

1. Export the answers to CSV or Excel.
2. In a spreadsheet, use AVERAGE, MEDIAN and MODE (MODE.MULT to find several modes).
3. For rating questions, also build a frequency table of answer options. It shows the mode at a glance and the shape of the distribution.
4. For a quick check without a spreadsheet, paste the numbers into the median and percentile calculator, which also returns quartiles and the IQR.

In SurveyNinja, the report for a Rating question shows the mean, median and standard deviation under the scale. It doesn't show the mode, so read the most common answer from the distribution chart.

Mean, median and mode are part of descriptive statistics, together with measures of spread and frequency tables.