SAT Math formula sheet · all 24 · Problem-Solving and Data Analysis · #15 of 24

Mean, median, mode, range and standard deviation on the SAT: How It Is Tested

One-variable data: distributions and measures of center and spread

Statistics diagram for the SAT: Know these 5 calculations for statistics. Mean, median, and standard deviation can be computed in Desmos. Range and mode
What it is really testingKnow these 5 calculations for statistics. Mean, median, and standard deviation can be computed in Desmos. Range and mode MUST be memorized, because Desmos will not do them for you.

The question from the sheet

Medium
SAT Problem-Solving and Data Analysisanswer B
d,14,18,e,27,39,fd, 14, 18, e, 27, 39, f
For the given data set, the data values are listed in ascending order, where dd, ee, and ff are constants. For this data set, the mean is 2424, the median is 2121, and the range is 5151. What is the value of ff?
A4949
✓5050
C5151
D9999

How the diagram applies

  1. Seven values in order, so the median is the 4th value: e=21e = 21.
  2. Mean 2424 means the sum is 7×24=1687 \times 24 = 168. The five known values add to 14+18+21+27+39=11914 + 18 + 21 + 27 + 39 = 119, so d+f=49d + f = 49.
  3. Range 5151 means f−d=51f - d = 51. Add the two equations: 2f=1002f = 100, so f=50f = 50.

Answer: B

That is 1 of 24.

The whole sheet is one page per formula, each one solved on a real SAT question. Print it, stick it on the wall, scan any diagram to get back here.

Download the sheet (PDF)Watch this one solved →

The PDF needs no account. The video, the clean diagrams and practice on this skill need a free one, and never a card.

All 24 diagrams

Common Questions

It comes up as an SAT one-variable data: distributions and measures of center and spread question. Know these 5 calculations for statistics. Mean, median, and standard deviation can be computed in Desmos. Range and mode MUST be memorized, because Desmos will not do them for you.

Seven values in order, so the median is the 4th value: e = 21. Mean 24 means the sum is 7 × 24 = 168. The five known values add to 14 + 18 + 21 + 27 + 39 = 119, so d + f = 49. Range 51 means f - d = 51. Add the two equations: 2f = 100, so f = 50.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Statistics is not one of them. It is one of the 24 things the test expects you to know without being given them. See what the reference sheet does cover at /blog/sat-math-reference-sheet.