Free ATI TEAS 7 Mathematics guide
October 2026 - Mean, Median, Mode & Range Study Guide for nursing students in
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.
The four measures
| Measure | How | Watch 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.
- Order first: 9, 9, 12, 14, 22, 51.
- Mean: the sum is 117, and
117 ÷ 6 = 19.5. - Median: six values, so average the third and fourth —
(12 + 14) ÷ 2 = 13. - Mode: 9, the only repeated value.
- 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.
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.
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.
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.
Review quiz
4 questions on this topic, each with the reasoning worked through. Pick an answer to see how it went, or open the explanation straight away.
-
Question 1 of 4
Find the median of: 18, 7, 25, 12, 7, 30.
Show the answer and explanation
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. -
Question 2 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?
Show the answer and explanation
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.
-
Question 3 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?
Show the answer and explanation
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.
-
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?
Show the answer and explanation
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.
Put this TEAS topic into practice
Build a set on statistics and use the rationale on every question to reinforce what you just reviewed.
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