Mean, Median, and Mode · Sub-skill drill
Computing and Manipulating the Mean
The mean of a list of n values is the sum of the values divided by n. The most useful identity for SAT mean problems is sum equals mean times count. Many SAT mean questions give you the mean and the count and ask for a missing value; rewrite the identity as sum = mean × count, plug in, then subtract the known values from the sum to recover the missing value. This identity-based approach is faster than recomputing the mean from scratch and avoids the rounding errors that creep into multi-step division.
How this sub-skill is tested on the SAT
The mean of a list of n values is the sum of the values divided by n. The most useful identity for SAT mean problems is sum equals mean times count. Many SAT mean questions give you the mean and the count and ask for a missing value; rewrite the identity as sum = mean × count, plug in, then subtract the known values from the sum to recover the missing value. This identity-based approach is faster than recomputing the mean from scratch and avoids the rounding errors that creep into multi-step division.
This sub-skill sits inside the broader Mean, Median, and Mode topic, which is part of the College Board's Problem Solving & Data Analysis content domain. Problem Solving and Data Analysis is where the SAT pretends to be the real world. Every question in this domain is wrapped in context: a recipe, a survey, a clinical trial, a lab measurement, a marketing report. The math itself is rarely harder than middle-school arithmetic — ratios, proportions, percentages, unit conversions, means, medians, scatter plots, two-way tables, and basic probability. What trips students up is the reading. The College Board has spent two decades calibrating these prompts to reward students who slow down on the setup and punish students who rush to compute. ScoreRe
Practice questions in this drill set
Below are 7 practice questions targeting this exact sub-skill, ordered from easier to harder. Each question is tagged with its target score band so you can focus on questions that match the band you are working out of. Worked solutions are open by default — read each one even if you got the question right, because the way the solution is structured often reveals a faster path than the one you used.
-
The values 12, 19, 11, 29, 22 were recorded in a science experiment. What is the mean of the data set?
- A 18.60
- B 93.00
- C 19.60
- D 19.00
Worked solution
Answer: A — 18.60
Sum the values: 12 + 19 + 11 + 29 + 22 = 93. Divide by the number of values, 5: 93 / 5 = 18.60.
-
The values 1, 1, 6, 21, 15 were recorded in a science experiment. What is the mean of the data set?
- A 6.00
- B 8.80
- C 44.00
- D 9.80
Worked solution
Answer: B — 8.80
Sum the values: 1 + 1 + 6 + 21 + 15 = 44. Divide by the number of values, 5: 44 / 5 = 8.80.
-
The values 5, 17, 23, 22, 2 were recorded in a science experiment. What is the mean of the data set?
- A 14.80
- B 69.00
- C 13.80
- D 17.00
Worked solution
Answer: C — 13.80
Sum the values: 5 + 17 + 23 + 22 + 2 = 69. Divide by the number of values, 5: 69 / 5 = 13.80.
-
The values 23, 27, 22, 3, 26 were recorded in a science experiment. What is the mean of the data set?
- A 101.00
- B 21.20
- C 23.00
- D 20.20
Worked solution
Answer: D — 20.20
Sum the values: 23 + 27 + 22 + 3 + 26 = 101. Divide by the number of values, 5: 101 / 5 = 20.20.
-
The values 14, 6, 18, 3, 10 were recorded in a science experiment. What is the mean of the data set?
- A 51.00
- B 10.00
- C 11.20
- D 10.20
Worked solution
Answer: D — 10.20
Sum the values: 14 + 6 + 18 + 3 + 10 = 51. Divide by the number of values, 5: 51 / 5 = 10.20.
-
The values 8, 22, 21, 24, 19 were recorded in a science experiment. What is the mean of the data set?
- A 21.00
- B 19.80
- C 18.80
- D 94.00
Worked solution
Answer: C — 18.80
Sum the values: 8 + 22 + 21 + 24 + 19 = 94. Divide by the number of values, 5: 94 / 5 = 18.80.
-
The values 7, 2, 24, 9, 22 were recorded in a science experiment. What is the mean of the data set?
- A 64.00
- B 12.80
- C 13.80
- D 9.00
Worked solution
Answer: B — 12.80
Sum the values: 7 + 2 + 24 + 9 + 22 = 64. Divide by the number of values, 5: 64 / 5 = 12.80.
Why this band assignment matters
Every question in this drill is tagged with a target score band — 400–500, 500–600, 600–700, or 700–800 — based on its difficulty and the patterns the College Board uses for questions at each level. If you are aiming to break out of a 580 plateau, the 600–700 questions in this drill are your highest-leverage practice. If you are chasing 750+, the 700–800 questions here are the ones that separate the top 10% of test takers from everyone else.
Use the band tags to filter your work. If you can confidently solve every 400–500 and 500–600 question without notes, move to the 600–700 set. If those land cleanly, the 700–800 set is your final boss. The worked solutions in this drill are written so that even the hardest questions become learnable patterns once you have seen the structure of the solve a few times.