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SAT Prep / Problem-Solving & Data Analysis / Data Distributions & Measures of Center
SAT Math · Problem-Solving & Data Analysis

Data Distributions & Measures of CenterHow the SAT tests it — and how to beat it

Mean, median, mode, range, and standard deviation — and how outliers or skew change them — read from lists, tables, and frequency plots.

Practice Data Distributions & Measures of Center FreeAll of Problem-Solving & Data Analysis

Data Distributions & Measures of Center in Our Question Bank

41

Total questions

14

Easy

16

Medium

11

Hard

What the SAT Actually Tests

These questions test mean, median, mode, range, and standard deviation as concepts, not just calculations: how does removing an outlier move the mean vs. the median? Which of two dot plots has a larger standard deviation? What's the median when data is given as a frequency table?

Know the behavioral rules: the mean chases outliers, the median resists them; skewed-right data pulls the mean above the median; standard deviation is about spread from the mean, not the height of bars. For frequency tables, find the median by counting positions — with 25 values, the 13th value in order is the median.

Real Data Distributions & Measures of Center Practice Questions

Straight from the Grind1600 question bank — try each one before revealing the answer.

Question 1easy
The range of a data set is the difference between the maximum and minimum values. What is the range of the following data set? 14, 22, 8, 31, 17, 25
  • A)8
  • B)17
  • C)31
  • D)23
Show answer & explanation

Correct answer: D

Choice D is correct. The maximum value is 31 and the minimum value is 8. The range is 31 - 8 = 23.

Question 2medium
A teacher recorded the test scores of 11 students: 62, 68, 71, 74, 78, 78, 82, 85, 88, 91, 95. If the score of 95 is removed from the data set, which of the following correctly describes the change?
  • A)The mean decreases and the median stays the same.
  • B)The mean stays the same and the median decreases.
  • C)Both the mean and the median decrease.
  • D)The mean decreases and the median increases.
Show answer & explanation

Correct answer: A

Choice A is correct. With 11 values, the mean is 872/11 ≈ 79.3 and the median is the 6th value: 78. Removing 95 gives 10 values with mean 777/10 = 77.7 (decreased) and median = average of 5th and 6th values = (78 + 78)/2 = 78 (unchanged).

Traps to Avoid

  • Finding the median of a frequency table by taking the middle category instead of the middle data value.
  • Assuming the mean must equal the median in any 'normal-looking' plot.
  • Comparing standard deviations by the range alone — clustering near the mean matters more than total width.

More Problem-Solving & Data Analysis Skills

Ratios, Rates & Units

Setting up proportions, converting units, and reasoning with rates — the most common word-problem machinery on the SAT Math section.

Percentages

Percent change, percent of a quantity, reverse-percentage problems, and multi-step percent scenarios like tax-plus-discount.

Scatterplots & Two-Variable Data

Reading scatterplots, lines of best fit, interpreting slope in context, and distinguishing linear from exponential association.

Probability

One-event and conditional probability, usually read out of two-way frequency tables — the key is identifying the correct restricted group.

Inference & Margin of Error

What sample results let you conclude about a population, how margin of error works, and why sample size changes confidence.

Evaluating Statistical Claims

Judging what a study design supports: random sampling vs. random assignment, causation vs. correlation, and generalizability.

Master Data Distributions & Measures of Center With Adaptive Practice

41 Data Distributions & Measures of Center questions with step-by-step explanations, woven into a day-by-day study plan built for your test date.

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