Mean, Median, Mode & Range
Summarize a set of biology measurements with one number for the center (mean, median, or mode) and one for the spread (range), and know when each is the honest choice.
A single experiment can produce dozens of numbers, and nobody can reason about a raw column of data. Measures of center squeeze all those values into one honest summary: the mean (the average) uses every value, the median (the middle value) ignores how extreme the ends are, and the mode (the most common value) reports what happened most often. The range (largest minus smallest) tells you how spread out the data is. Which one you pick is not a style choice, it is an ethics choice: report the mean of a skewed dataset and you can make a typical result look far bigger than it is. Epidemiologists report median recovery times because a few very long cases would inflate the mean. Biostatisticians choose the median income or median tumor size when one huge outlier would mislead. Lab scientists average replicate readings to smooth out noise, and doctors reading a study need to know whether the headline number is a mean or a median before they trust it. Learn this and you can both summarize your own data honestly and catch a misleading summary in someone else's.
- Common Core · HSS-ID.A.2Use statistics appropriate to the shape of the data to compare the center (median, mean) and spread (range, interquartile range) of two or more data sets.
- Common Core · HSS-ID.A.3Interpret differences in shape, center, and spread in the context of the data, accounting for the effect of extreme data points (outliers).
- Ohio · Ohio HS S.ID.2Summarize a single set of numerical data using measures of center (mean, median) and spread (range), and interpret them in context.
- NGSS · SEP-4Analyzing and Interpreting Data: use mean, median, mode, and range to describe and compare data sets and to identify how outliers affect a summary.
- AP · AP Bio SP 6 (Statistical Tests and Data Analysis)Describe data with an appropriate measure of center and spread, and justify the choice given the distribution of the data.
- Add a list of numbers and divide: The mean is a sum divided by a count, so students must add accurately and divide by the number of values.
- Put numbers in order from least to greatest: The median is the middle of an ordered list, so students must be able to sort values before finding it.
- Subtract to find a difference: The range is the largest value minus the smallest, so students must subtract to measure spread.
Prerequisites are inferred: pending teacher review.
Re-learn the skill with worked practice and clear examples.
Practice computing each measure from a real biology data set: average with the mean, order and take the middle for the median (averaging the two middles when the count is even), and subtract for the range. Work slowly and check each number.
| Beetle | Mass (g) |
|---|---|
| A | 3 |
| B | 5 |
| C | 4 |
| D | 6 |
| E | 7 |
| Sum | 25 |
| Mean (25 ÷ 5) | 5 |
Using the table, find the mean mass of the five beetles.
Reviewed| Beetle | Mass (g) |
|---|---|
| A | 3 |
| B | 5 |
| C | 4 |
| D | 6 |
| E | 7 |
- A.4 g
- B.5 g
- C.6 g
- D.25 g
Show the worked solution ▾
Answer: B. 5 g
- Step 1: Add the masses: 3 + 5 + 4 + 6 + 7 = 25 grams.
- Step 2: Divide by the count: There are 5 beetles, so the mean is 25 divided by 5 = 5 grams.
Why it's right: The mean is the sum divided by the count: 25 grams divided by 5 beetles is 5 grams.
- A: This divides by 6 or miscounts the beetles; the correct count is 5.
- C: This is too high; 25 divided by 5 is 5, not 6.
- D: 25 g is the sum of all the masses, not the average.
Aligned to Common Core HSS-ID.A.2: measures of center (mean) · reading level ~grade 9
Five students record their pulse in beats per 10 seconds: 8, 3, 5, 9, 4. What is the median?
Reviewed- A.4
- B.5
- C.6
- D.8
Show the worked solution ▾
Answer: B. 5
- Step 1: Put the values in order: Ordered from least to greatest: 3, 4, 5, 8, 9.
- Step 2: Take the middle value: With five values, the third one is the middle. That value is 5.
Why it's right: Once ordered as 3, 4, 5, 8, 9, the middle value is 5, so the median is 5.
- A: 4 is the second value in the ordered list, not the middle.
- C: 6 is not even in the data set; it may come from averaging without ordering.
- D: 8 is a large value from the original unordered list, not the middle of the ordered list.
Aligned to Ohio HS S.ID.2: measures of center (median, odd count) · reading level ~grade 9
Four enzyme reactions finish in these times (seconds): 6, 10, 4, 8. What is the median?
Reviewed- A.6
- B.7
- C.8
- D.10
Show the worked solution ▾
Answer: B. 7
- Step 1: Order the values: Least to greatest: 4, 6, 8, 10.
- Step 2: Average the two middle values: With four values, the two middles are 6 and 8. Their average is (6 + 8) divided by 2 = 14 divided by 2 = 7.
Why it's right: For an even count, the median is the average of the two middle values: (6 + 8) divided by 2 = 7.
- A: 6 is only one of the two middle values; you must average both.
- C: 8 is only the other middle value; you must average both, not pick one.
- D: 10 is the largest value, not the middle of the ordered list.
Aligned to Common Core HSS-ID.A.2: measures of center (median, even count) · reading level ~grade 9
- A student averages five replicate absorbance readings so one shaky measurement does not decide the result on its own.
- A team orders their reaction times and reports the median so a single very slow trial does not distort their summary.
- A field biologist subtracts the smallest wing length from the largest to report the range of a captured sample.
Fill these in as you work through the lesson.
- Mean (sum divided by count):
- Median (middle value when ordered):
- Mode (the most common value):
- Range (largest minus smallest):
To find the mean, add every value and divide by the . To find the median, put the values in and take the value. When the data has an , the median is usually the more honest center because the mean gets pulled toward the extreme value.
- For 68, 72, 75, 75, 90, compute the mean, the median, and the mode, and say which two are different and why.
- Explain in one sentence why adding a single very large value changes the mean a lot but changes the median very little.
- You measure five reaction times and one trial was clearly a fluke that ran long. Which measure of center should you report, and why?
A set is 20, 21, 22, 23, 90. Add them: 20 + 21 + 22 + 23 + 90 = 176, then divide by 5 to get the mean = ____. Order them and take the middle value to get the median = ____. Because 90 is an outlier, the ____ better represents a typical value.
The vocabulary of this topic, shown in the way you will meet it.