Digital SAT · Statistics & Data Distribution
How to Solve Mean, Median, and Range on the Digital SAT
Three quick measures: the mean is the sum over the count, the median is the middle of the ordered list, and the range is the largest minus the smallest. Order the data first, then read or compute the one asked. If a value is added or removed, only the affected measure changes, so recompute just that. For long lists, drop the data into Desmos and use mean or median directly.
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- typical difficulty
- Easy to medium typical difficulty
- practice questions
- 99 practice questions
Frequency reflects how often this question type appears on a full-length Digital SAT. The difficulty mix reflects every question of this type across our bank.
What the question bank shows
Sorting is required for the median and the range; the mean is sum over count.
Type the data and use mean() or median() for an exact value.
Only the affected measure changes; edit the list and reread it.
How to recognize mean, median, and range questions
- A data set arrives as a list, a table, or a frequency table, and a center or spread is asked.
- The words mean, average, median, mode, or range appear.
- A value is added, removed, or changed, and you compare the new statistic to the old.
- Choices are numbers, and some are grid-ins.
Why students miss these
The step-by-step method
- 1
Order the data
Sort into increasing order before finding a median or range, since position matters.
- 2
Use the right formula
Mean is sum over count; median is the middle value, or the average of the two middle for an even count; range is largest minus smallest.
- 3
Weight and adjust
In a frequency table, weight each value by its frequency; when a value is added or removed, recompute only the affected measure.
- 4
Answer the exact measure
Confirm you reported the specific one the question named.
Solving it on Desmos
- Enter the data as a list. Type it in Desmos, like D = [4, 7, 7, 9, 12, 15, 18].
- Use the built-in functions. Type mean(D) or median(D) for the value, with no hand arithmetic.
- Edit for changes. Add or remove a value in the list and read the new statistic instantly.
Full Desmos walkthrough for mean, median, and range→
Worked examples
Medium example
A data set of 6 numbers has a mean of 15.
A: Incorrect. This is the original mean, ignoring the removal.
B: Incorrect. This results from dividing the new sum by 6 instead of 5.
C: Correct. The original sum is ; removing 9 gives , and .
D: Incorrect. This results from subtracting too much from the original sum.
Explanation
New mean .
Detailed explanation
The original sum is ; removing 9 leaves a sum of 81 over 5 values, so the mean is .
Medium example
The data set 5, 8, 8, 11, and 18 has its largest value increased by 10.
A: Correct. The total increases by 10 spread over 5 values, so the mean increases by .
B: Incorrect. This divides the increase by 2 rather than by the 5 values.
C: Incorrect. This is unrelated to spreading the increase across the values.
D: Incorrect. This is the increase in the total, not the increase in the mean.
Explanation
Mean increase .
Detailed explanation
Adding 10 to one value raises the sum by 10, and dividing that change across the 5 values increases the mean by .
Hard example
A: Incorrect. 7 is the mode, not the middle value.
B: Correct. With 7 values in order, the median is the 4th value, which is 9.
C: Incorrect. 10 is the mean, not the median.
D: Incorrect. 12 is the 5th value, not the middle.
Explanation
7 ordered values; the 4th (middle) is 9.
The common traps
| Pattern | What it does | The tell |
|---|---|---|
| Median without ordering | Took the middle of the list as written. | Sort before reading a median or range. |
| Even-count median | Picked one middle value when the count is even. | With an even count, the median averages the two middle values. |
| Ignored frequency | Counted each row once in a frequency table. | Weight every value by how many times it occurs. |
| Wrong measure | Reported the mean when the median or range was asked. | Match the answer to the measure named. |
Try it: two real questions
What is the mean of the data set 4, 7, 9, and 10?
What is the median of the data set 3, 5, 5, 8, and 9?
Question 3 is ready when you are
Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.
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Related reading
Common questions
How do you find the median on the SAT?
Order the data, then take the middle value; for an even count, average the two middle ones. In Desmos, type the data as a list and use median(list).
How do I find the mean of a data set?
Add all the values and divide by how many there are. For long lists, enter the data in Desmos and type mean(list) to avoid a summing slip.
How does adding or removing a value change the mean?
Recompute the sum and count with the change, then divide. In Desmos, edit the list and read the new mean rather than redoing the whole sum.
How do I read a frequency table for the mean?
Multiply each value by its frequency, add those products, and divide by the total frequency. Each value counts as many times as its frequency.
What is the range of a data set?
The largest value minus the smallest. Order the data first so the extremes are easy to read, then subtract.
Practice mean, median, and range the way it is tested
Start with the free 16-question diagnostic, then drill this type with step-by-step reasoning on every question.
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