How to find the mean, median, mode and range
TEAS 7 outline: Use statistics to evaluate data sets, tables, charts and graphs
Also covers HESI A2 Math (Mean, median, mode)
- Mean = sum of values ÷ number of values.
- Median is the middle value after you put the data in order.
- Mode is the most common value; range is largest minus smallest.
- Total = mean × count, which helps you find a missing value.
- An outlier pulls the mean toward it but barely moves the median.
Key facts
- Mean = sum of the values ÷ number of values; it must land between the smallest and largest value.
- Total = mean × number of values, which lets you work backward to a missing value.
- Median: put the values in order first; with an even count, average the two middle values.
Show all 7 key factsShow fewer
- Mode is the most frequent value; a set can have no mode or more than one mode, and the mode also works for categories.
- Range = largest value − smallest value; it measures spread, not center.
- An outlier pulls the mean toward it but barely moves the median, so the median is usually the better center when there are outliers.
- Skewed right (long tail toward high values): mean usually above median. Skewed left: mean usually below median. Symmetric: mean and median about equal.
Quick check1 question · 2 more at the end
A phlebotomist recorded the number of blood draws she completed on each of seven shifts: 14, 9, 22, 17, 9, 19, 12. What is the range of the data?
Correct answer: B.
The range is the largest value minus the smallest value. Here the largest is 22 and the smallest is 9, so the range is 22 − 9 = 13 draws. The range measures how spread out the data are, not where the center is.
A This is the median (the middle of the ordered list 9, 9, 12, 14, 17, 19, 22), not the range.
B Correct: 22 − 9 = 13.
C This is the mode, the value that appears most often, and also the smallest value.
D This is the largest value alone; the range subtracts the smallest value from it.
Full lesson
Each part starts with its main idea. Open a part when you want the details.
The short answer: The mean is the sum of the values divided by how many there are. The median is the middle value after you put the data in order. The mode is the value that appears most often, and the range is the largest minus the smallest. An outlier pulls the mean toward it but barely moves the median.
1 What do the mean, median and mode each tell you?Mean, median and mode each describe a "typical" value, while the range shows how spread out the data are. 1 min
Mean, median and mode each describe a "typical" value, while the range shows how spread out the data are.
| Measure | How to find it | Best for |
|---|---|---|
| Mean | Add all values, divide by how many | Balanced data with no extreme values |
| Median | Put in order, take the middle | Data with outliers or a long tail |
| Mode | The value that appears most often | The most common value, or categories |
| Range | Largest minus smallest | How spread out the data are |
2 How do I find the mean?The mean is the total shared out equally among all the values. 1 min
The mean is the total shared out equally among all the values.
Example 1. A nurse recorded five patients' wait times in minutes: 12, 8, 15, 10, 20.
- Add: 12 + 8 + 15 + 10 + 20 = 65.
- Count the values: 5.
- Divide: 65 ÷ 5 = 13 minutes.
- Check: 13 sits between the smallest (8) and the largest (20).
Classic wrong turn: dividing by the wrong count after skipping a value. Count the values twice.
The one rule to remember: total = mean × number of values. It works backward too. If 4 shifts averaged 30 patients, they saw 4 × 30 = 120 patients in all.
3 How do I find the median, mode and range?The median is the middle value, but only after the data are in order. 1 min
The median is the middle value, but only after the data are in order.
Example 2. Six students reported last night's hours of sleep: 7, 5, 8, 6, 9, 6.
- Order: 5, 6, 6, 7, 8, 9.
- Six is an even count, so there are two middle values: 6 and 7.
- Median: (6 + 7) ÷ 2 = 6.5 hours.
- Mode: 6 appears twice, more than any other value, so the mode is 6.
- Range: 9 − 5 = 4 hours.
Classic wrong turn: averaging the middle of the list as written (8 and 6) without ordering it first.
If every value appears once, there is no mode. If two values tie for most frequent, both are modes.
4 What happens when there is an outlier?An outlier pulls the mean toward it but barely moves the median. 1 min
An outlier pulls the mean toward it but barely moves the median. An outlier is a value far away from the rest of the data.
Example 3. Five front-desk workers earn $18, $19, $20, $21 and $22 an hour. Then a manager earning $70 an hour is added.
| 5 workers | 6 workers (with $70) | |
|---|---|---|
| Mean | 100 ÷ 5 = $20 | 170 ÷ 6 ≈ $28.33 |
| Median | $20 | (20 + 21) ÷ 2 = $20.50 |
| Range | 22 − 18 = $4 | 70 − 18 = $52 |
- The mean jumped by more than $8.
- The median moved only 50 cents.
- The range grew the most, because it uses the extreme value directly.
Classic wrong turn: calling $28.33 the "typical" pay. Five of the six people earn $22 or less, so the median describes this group better.
5 Which center should I use?Use the mean for balanced data, the median for lopsided data, and the mode for categories. 1 min
Use the mean for balanced data, the median for lopsided data, and the mode for categories.
- Symmetric: both sides mirror each other, and the mean and median are about equal.
- Skewed right: a long tail toward high values, like the pay example. The mean is usually pulled above the median.
- Skewed left: a long tail toward low values. The mean is usually pulled below the median.
- Categories (such as the most requested appointment day): only the mode makes sense.
Common mistakes
The traps students fall into most. Read these before you practice.
Watch out: Find the median of the ordered list, not the middle of the list as written.
Watch out: With an even number of values, the median is the average of the two middle values, not just one of them.
Watch out: Range is largest minus smallest, not the largest value by itself.
Watch out: Divide the total by the number of values, not by the number of rows or categories.
Watch out: Changing one value changes the mean by (the change in that value) ÷ (number of values), not by the full change.
How to remember it
Picture the median as the strip down the middle of a highway. One car (an outlier) swerving far off the road does not drag the strip with it. It does drag the average position of all the cars (the mean). Mode sounds like "most."
Self-check:
- Find the mean and median of 4, 9, 6, 5, 6.
- Three quiz scores average 80. What is their total?
- Add 40 to the set in question 1. Which changes more, the mean or the median?
Show answers
- Mean 6, median 6.
- Add: 4 + 9 + 6 + 5 + 6 = 30. Count: 5 values.
- Mean: 30 ÷ 5 = 6.
- Order: 4, 5, 6, 6, 9. The middle value is 6.
- 240.
- Total = mean × number of values: 80 × 3 = 240.
- The mean changes more.
- New set in order: 4, 5, 6, 6, 9, 40. Total: 30 + 40 = 70. Count: 6.
- New mean: 70 ÷ 6 ≈ 11.67, up from 6.
- New median: six values, so average the two middle ones: (6 + 6) ÷ 2 = 6. It did not move.