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Statistics (center, spread, plots) — SHSAT practice questions

On the SHSAT, Statistics (center, spread, plots) covers mean, median, range, and how a data set changes when a value is added or replaced. A student has to recover a missing score from a changed average, find a mean when two people share the same total but a different number of trials, and recompute the median after one entry is swapped. Questions are word problems about bowling, quizzes, or reports; plots, when they appear, still ask for a center or spread. Traps include treating a total as an average, forgetting to reorder before naming the middle value, and mixing mean with median. Answer choices are single numbers matching those mistakes.

  • Section: Mathematics 57 questions on the paper
  • 111 practice questions in the app

Sample questions

Question 1

The average of 4 quiz scores is 84. After a fifth quiz score is included, the average becomes 86. What is the fifth quiz score?

  1. A88
  2. B90
  3. C94
  4. D96
Show answer

Answer: C — 94

The first 4 scores total 4⋅84=3364\cdot84=336. The 5 scores total 5⋅86=4305\cdot86=430. The fifth score is 430−336=94430-336=94.

Question 2

The numbers of pages in 7 reports are 8,12,15,15,18,22,8,12,15,15,18,22, and 29. If the report with 29 pages is replaced by a report with 16 pages, what is the median number of pages?

  1. A15
  2. B16
  3. C17
  4. D18
Show answer

Answer: A — 15

After the replacement, the ordered data are 8,12,15,15,16,18,22. With 7 values, the median is the fourth value, which is 15.

Question 3

In a bowling league, Marcus bowled 3 games with a mean score of 150. Elena bowled 6 games. If Marcus and Elena rolled the same total pinfall, what was Elena's mean score per game?

  1. A75
  2. B90
  3. C112.5
  4. D150
Show answer

Answer: A — 75

Marcus's total pinfall is 3×150=450. Since Elena's total pinfall is also 450 but spread over 6 games, her mean score is 450÷6=75.

Practice 111 Statistics (center, spread, plots) questions in the app

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