VTCAP Grade 9 Statistics and Probability Practice

VTCAP Grade 9 Statistics and Probability. Practice it free.

High school statistics content reported as the 'Statistics and Probability' performance indicator; blueprint target: 6-10 points (13-20% of the grade 9 test). The grade 9 Performance Level Descriptors publish the assessed focus area listed below (one-variable displays, center and spread, two-way tables, scatterplots, fitted functions, correlation, and causation). This Grade 9 reporting domain maps to 7 practice skills and 8 representative questions from the playable bank.

Grade 97 mapped skills

Statistics and Probability skills

Interpret Categorical and Quantitative Data

Standards basis

Common Core State Standards for Mathematics (CCSS-M) — Vermont

How the VTCAP reports it

Vermont administered the Smarter Balanced summative through spring 2022, then replaced it with the Cognia-developed Vermont Comprehensive Assessment Program (VTCAP) beginning spring 2023 — this landing slug predates the switch. VTCAP mathematics is an adaptive, CCSS-M-aligned assessment in grades 3-9. It is NOT a Smarter Balanced administration: its reporting categories are groupings of the CCSS grade-level domains (e.g. 'The Number System, Expressions and Equations'), not SBAC claims, though two cross-grade Mathematical Practices indicators ('Problem Solving, Reasoning, and Argument'; 'Modeling, Patterns, and Structure') echo the old claim structure. Per the test specifications, the grades 3-8 test may assess any CCSS-M standard at the grade; the grade 9 test assesses a prioritized subset of the high school CCSS-M within the conceptual categories of Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability (the assessed focus areas are published in the grade 9 Performance Level Descriptors).

Blueprint & weighting

VTCAP Test Specifications (Spring 2026) operational test blueprint, target percent of points per grade — Grade 3: OA 24-35%, NBT 10-14%, NF 16-20%, MD 22-29%, G 6-10%, constructed-response Mathematical Practices 12%. Grade 4: OA 20-31%, NBT 16-20%, NF 20-31%, MD 12-20%, G 6-10%, practices 12%. Grade 5: OA 14-22%, NBT 14-25%, NF 22-29%, MD 20-27%, G 8-16%, practices 12%. Grade 6: RP 15-22%, NS 15-22%, EE 15-22%, G 11-19%, SP 11-19%, practices 11%. Grade 7: RP 15-22%, NS 11%, EE 15-30%, G 11-19%, SP 19-22%, practices 11%. Grade 8: F 18-29%, NS 7%, EE 20-31%, G 18-29%, SP 18-22%, practices 11%. Grade 9 (all machine-scored): Number and Quantity/Algebra 18-27%, Algebra/Functions 31-40%, Geometry 20-29%, Statistics and Probability 13-20%; the two practices indicators are dual-aligned targets of >18% of points each. Identical figures appear in the Spring 2025 specifications.

Official sources

VTCAP Test Specifications, Spring 2026 (Vermont AOE / Cognia)
VTCAP Test Specifications, Spring 2025 (Vermont AOE / Cognia)
VTCAP Performance Level Descriptors: Mathematics, Grades 3-9 (Vermont AOE)

8 free questions · 0/0 correct

Practice playeasy

Four small data sets are listed below. Which set has the least standard deviation?

Set A: $7, 9, 11, 13$
Set B: $8, 10, 10, 12$
Set C: $5, 10, 10, 15$
Set D: $6, 9, 11, 14$

Set B has mean $10$ with two values at the mean and the others only two units away, giving the smallest standard deviation, about $1.4$ . Sets A, C, and D spread farther from their means.

Practice playeasy

The distances, in miles, run on seven days are $6\textsf{,}$ $8\textsf{,}$ $12\textsf{,}$ $9\textsf{,}$ $14\textsf{,}$ $7\textsf{,}$ and $14\textsf{.}$ Which data set has the same mean?

The original mean is $\dfrac{6 + 8 + 12 + 9 + 14 + 7 + 14}{7} = 10$ . The set $4\textsf{,}$ $6\textsf{,}$ $8\textsf{,}$ $10\textsf{,}$ $12\textsf{,}$ $14\textsf{,}$ $16$ also has mean $10$ , so the means match.

Practice playeasy

Five afternoon temperatures, in degrees Fahrenheit, are $64\textsf{,}$ $78\textsf{,}$ $72\textsf{,}$ $60\textsf{,}$ and $66\textsf{.}$ Which data set has the same median?

In order, the original values have middle value $66$ , so the median is $66$ . The set $61\textsf{,}$ $65\textsf{,}$ $66\textsf{,}$ $77\textsf{,}$ $81$ also has median $66$ , so the medians match.

Practice playeasy

On four science quizzes, Priya earned scores of $85$ , $92$ , $78$ , and $88$ . On a fifth quiz, her score was $x$ . The mean score on all five quizzes is $87$ . What is the value of $x$ ?

Five quizzes with a mean of $87$ total $5 \times 87 = 435$ . Since $85 + 92 + 78 + 88 = 343$ , $x = 435 - 343 = 92$ .

Practice playeasy

A box plot summarizes the data 2, 4, 5, 7, 9, 11, 13. Find the median.

Order the data; the middle value is $7$ .

Practice playeasy

For a normal distribution, approximately what percent of the data lies within $2$ standard deviations of the mean? Use the empirical rule.

By the empirical rule, about $95\%$ of the data lie within $2$ standard deviations of the mean.

Practice playeasy

A coach records the goals her team scored in seven games: $1, 3, 2, 3, 0, 3, 2$ . What is the mode of the data?

The value $3$ appears three times, more often than any other value, so the mode is $3$ .

Practice playeasy

Four data sets show minutes spent on homework each night. Which set has the greatest standard deviation?

Set A: $18, 20, 22, 24, 26$
Set B: $19, 21, 23, 25$
Set C: $15, 20, 25, 30$
Set D: $20, 21, 22, 23, 24$

Set C has mean $22.5$ with values stepping by $5$ from $15$ to $30$ , so each value is far from the center; its standard deviation is about $5.6$ . Sets A and B spread less evenly, and Set D is tightly clustered.