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150 multiple-choice questions and 85 flashcards, organised into 4 chapters, written to the Common Core State Standards blueprint. Every question carries a full rationale.
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Common Core State Standards (CCSS) — Mathematics, Grade 6: Statistics and Probability (6.SP.A.1-3, 6.SP.B.4-5). Public standards from corestandards.org.
CoStudy's 6th Math: Statistics & Probability bank holds 235 items organised into 4 chapters that follow the published blueprint. Every multiple-choice question carries a written rationale explaining why the correct answer is correct and why each distractor is tempting but wrong.
Each chapter follows a domain of the published exam outline. Practise one on its own:
A sample of 12 multiple-choice questions from the bank, with the full rationale shown.
A histogram shows:
Answer: A — Frequencies in intervals (bins) for quantitative data — bars touch
A) Standard. B) Bar graph. C/D) Different.
On a box plot, if the median line is on the LEFT side of the box, the data are:
Answer: B — Skewed right (more variability in the upper half)
Median closer to Q1 means more spread above median → skewed right. (A), (C), (D) misread.
A student summarizes data as: 'Mean is 50, IQR is 10.' What is missing?
Answer: A — The number of observations and units
A) 6.SP.B.5 requires n, attribute, and units alongside center and spread. B) Max alone is not required. C) Mode is optional. D) Reporting two means is unusual.
A box plot visually displays:
Answer: C — The five-number summary
C) Min, Q1, median, Q3, max — plus outliers as separate points. A/B/D) Single statistics, not the whole summary.
A sample with variability is shown by:
Answer: A — Values that differ from each other (spread)
A) Standard. B/C/D) Each is incorrect.
Range of 5, 8, 12, 15:
Answer: B — 10
B) Max − min = 15 − 5. A/C/D) Each is incorrect.
Add 1 outlier of 1000 to {2, 4, 6, 8}. The new mean is:
Answer: C — 204
Sum = 1020. /5 = 204. (A) is original mean; (B), (D) miscalculate.
The mean of {3, 5, 7, 9, 11} is:
Answer: A — 7
A) Sum = 35; 35 / 5 = 7. B/C) Single values, not averages. D) The maximum.
You collected ages of 20 people and reported only 'mean age = 12.' What concern does this raise?
Answer: D — Without spread/shape info, two very different age distributions could share this same mean
D) Spread and shape are essential — 50,50,50 and 0,50,100 share a mean. A) Numerical, not categorical. B/C) Both true, but the headline issue is that summarization is incomplete.
Removing the outlier 50 from {10, 12, 12, 14, 50} changes the mean from 19.6 to:
Answer: D — 12.0
D) New sum = 10+12+12+14 = 48; 48/4 = 12.0. A) The original mean. B) Off by two. C) Off by one.
In a distribution, the "center" is most commonly measured by:
Answer: C — The mean or the median
C) Mean and median are the standard centers. A) Mode is a center but rarely the headline. B) Range measures spread, not center. D) An extreme, not a center.
In a histogram, the vertical axis usually shows:
Answer: D — Frequency (count) of values in each bin
D) Height = frequency. A) Bin width is on the x-axis. B) Quartiles relate to box plots. C) Mean is a number, not an axis.
6 sample cards from the 85 in the bank.
Can a data set have two modes?
Yes — it's called 'bimodal' (two values tied for most common).
What is 'range'?
The difference between the largest and smallest values. Range = max − min.
Worked example — A histogram of test scores has bin heights 2, 5, 9, 6, 3 from low to high. Is it symmetric or skewed?
Step 1: List the bar heights left → right: 2, 5, 9, 6, 3. Step 2: The tallest bar is in the middle (9). Step 3: Compare the two sides. Left of peak: 2, 5. Right of peak: 6, 3. Approximately mirror — both descend. Step 4: Heights drop off similarly on both sides → symmetric (roughly mound-shaped). Answer: approximately symmetric.
What is Q3?
Median of upper half — 75th percentile.
What is Q1?
Median of lower half — 25th percentile.
What are the 'measures of center'?
Mean, median, and mode. They describe a typical or middle value.
These samples are a small slice. The full bank runs flashcards, multiple choice and timed mock exams with per-chapter progress tracking, on the web and in the iOS app.
Open 6th Math: Statistics & Probability →
The 6th Math: Statistics & Probability bank holds 235 items: 150 multiple-choice questions, 85 flashcards. 18 of them are on this page to read free, with no signup.
Yes. Every multiple-choice item carries a written rationale that states the controlling principle behind the correct answer and then addresses each wrong option in turn — why it tempts and precisely where it fails. Knowing why the plausible answer was wrong is worth more than knowing which letter was right.
It is organised into 4 chapters that follow the published exam blueprint: Statistical Questions and Variability; Distributions: Center, Spread, and Shape; Measures of Center and Variability; Displaying and Summarizing Data (Dot Plots, Histograms, Box Plots). The number of questions in each chapter is proportional to that domain's published weight, so working through the bank exposes you to roughly the mix the real exam uses.
Common Core State Standards (CCSS) — Mathematics, Grade 6: Statistics and Probability (6.SP.A.1-3, 6.SP.B.4-5). Public standards from corestandards.org.
The samples on this page are free to read in full, rationales included, with no account. The complete 235-item bank, the timed mock exams and per-chapter progress tracking are part of CoStudy on the web and in the iOS app.
Last reviewed 2026-08-22. Banks are written against the certifying body's published exam outline and re-checked when that outline changes — exams get renumbered, retired and reweighted, and a bank written to a superseded outline teaches the wrong proportions. Figures that are re-indexed annually are deliberately not asserted as rules; the questions test the governing principle instead.