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November 2026 - Mean, Median, Mode & Range Study Guide

Mean is the average, median is the middle value of an ordered list, mode is the most frequent, and range is the highest minus the lowest. The distinction that earns marks is that the median resists outliers where the mean does not.

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Updated November 2026

Mathematics guide Measurement and data · 16 scored questions 6 min read

Practice As You Read

Try 4 short questions throughout this guide. Check each answer to learn from the explanation.

0 of 4 questions answered No answers checked yet
Four contrasting data displays: separated category bars, touching histogram intervals, a connected time sequence and an unconnected scatter pattern.
Reading a statistic starts with knowing what was measured and how it is displayed; a graph’s structure tells you whether the data are categorical, continuous, ordered or paired.

The four measures

MeasureHowWatch for
Mean Add all values, divide by how many One extreme value drags it a long way
Median Order the values; take the middle one With an even count, average the middle two
Mode The value that occurs most often There can be none, one, or several
Range Highest minus lowest It is a single number, not a pair of values

Order the list before finding the median. Taking the middle of an unordered list is the most frequent error in this topic, and because the wrong value is genuinely in the data set it always appears among the choices.

All four from one data set

Worked example

Waiting times in minutes: 14, 9, 22, 9, 51, 12.

  1. Order first: 9, 9, 12, 14, 22, 51.
  2. Mean: the sum is 117, and 117 ÷ 6 = 19.5.
  3. Median: six values, so average the third and fourth — (12 + 14) ÷ 2 = 13.
  4. Mode: 9, the only repeated value.
  5. Range: 51 - 9 = 42.

Mean 19.5, median 13, mode 9, range 42. The mean sits above four of the six values because of the 51 — which is exactly why the median is the better summary here.

Question 1 of 4

Find the median of: 18, 7, 25, 12, 7, 30.

Answer Choices for Question 1

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Correct answer: B. 15

Ordered, the set is 7, 7, 12, 18, 25, 30, and with six values the median is the average of the third and fourth: (12 + 18) ÷ 2 = 15. 12 is the middle of the unordered list, 7 is the mode, and 16.5 is the mean.

Why outliers matter

An outlier is a value far from the rest. The mean uses every value, so one outlier moves it; the median only cares about position, so it barely notices. In the example above, replacing the 51 with 200 pushes the mean to 44.3 and leaves the median at 13.

That is why questions about income, waiting times or lengths of stay ask which measure is more representative. Where the data has a long tail, the median is the honest answer.

Question 2 of 4

A ward's lengths of stay in days are: 2, 3, 3, 4, 4, 5, 41. Which measure best represents a typical stay?

Answer Choices for Question 2

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Correct answer: B. The median, because the 41 drags the mean above almost every actual stay

The mean is 8.9 days, longer than six of the seven stays, while the median of 4 sits among the real values. Using every value is the mean's weakness here rather than its strength; the range describes spread rather than a typical case; and the mode is a legitimate measure but not automatically the most reliable.

Working backwards from a mean

A common question type gives you a mean and asks for a missing value. The trick is to work with the total rather than the average.

  • Multiply the mean by the number of values to get the total the set must sum to.
  • Add up the values you know.
  • Subtract to find the missing one.
  • For "what score is needed to reach an average of X", this is the whole method.

Weighted averages

When groups are different sizes, you cannot average their averages. Two wards with mean stays of 4 and 10 days do not give an overall mean of 7 unless they hold the same number of patients.

Instead, multiply each mean by its group size, add those products, and divide by the total number. With 30 patients at 4 days and 10 at 10 days: (30 × 4) + (10 × 10) = 220, over 40 patients, giving 5.5 days.

Terms to know

Mean
The sum of the values divided by how many there are.
Median
The middle value of an ordered list.
Mode
The most frequently occurring value.
Range
The highest value minus the lowest.
Outlier
A value far from the rest of the data.
Weighted average
A mean that accounts for groups of different sizes.
Measure of central tendency
A single value summarising a data set: mean, median or mode.

What the TEAS asks most

The same core ideas appear in different wording. If you can answer these without stopping to think, you have what this section requires.

Find the mean, median, mode or range of this set.

Order the list first — it costs five seconds and prevents the commonest error.

Which measure best represents this data?

The median, whenever there is an extreme value or a long tail.

What score is needed to bring the average up to X?

Multiply the target mean by the number of values, then subtract what you already have.

How does adding this value change the mean and the median?

The mean shifts towards the new value; the median moves only if the middle position changes.

Question 3 of 4

A student has scored 68, 74 and 80 on three tests. What is needed on a fourth to reach an average of 76?

Answer Choices for Question 3

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Correct answer: C. 82

Four tests averaging 76 require a total of 304, and the three scores so far sum to 222, leaving 82. Answering 76 assumes the target average is itself the score needed, which only holds when the current average is already on target.

Key points

  • Mean adds and divides; median is the middle of an ordered list; mode is the most frequent; range is a subtraction.
  • Always order the data before finding a median.
  • With an even number of values, the median is the average of the middle two.
  • The median resists outliers; the mean does not.
  • To find a missing value from a mean, work with the total rather than the average.

Question 4 of 4

Ward A has 20 patients with a mean stay of 3 days. Ward B has 5 patients with a mean stay of 13 days. What is the mean stay across both wards?

Answer Choices for Question 4

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Correct answer: B. 5 days

Total days come to (20 × 3) + (5 × 13) = 125, spread over 25 patients, giving 5 days. Averaging 3 and 13 to get 8 ignores that Ward A holds four times as many patients — the error a weighted average exists to prevent.

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