NY State Math Grades 3–8 Statistics and Probability Practice

Statistics and Probability skills

Develop understanding of statistical variability

Summarize and describe distributions

Investigate patterns of association in bivariate data

Use random sampling to draw inferences about a population

Investigate chance processes and develop, use, and evaluate probability models

Standards basis

New York State Learning Standards / New York State Next Generation Learning Standards (NGLS) — New York

How the NY State Math reports it

New York’s Grades 3–8 math tests and Regents math exams are state-developed assessments rather than a shared national framework. The grades 3–8 exams are aligned to New York State learning standards, and the Regents math sequence includes Algebra I, Geometry, and Algebra II, with the June 2026 Algebra II exam explicitly based on the New York State Next Generation Learning Standards.

Blueprint & weighting

Grades 3–8: the official page and the retrieved administration guide describe item/credit structure and timing, but no published domain-by-domain blueprint weighting was located in the primary sources used here. Regents (high school): NYSED publishes a per-conceptual-category 'percent of test by credit' blueprint for each course in its Educator Guides. Algebra I — Number & Quantity 4%–10%, Algebra 48%–61%, Functions 24%–32%, Statistics & Probability 7%–15%. Geometry (single conceptual category, by domain) — Congruence (G-CO) 27%–34%, Similarity, Right Triangles, & Trigonometry (G-SRT) 29%–37%, Circles (G-C) 2%–8%, Expressing Geometric Properties with Equations (G-GPE) 12%–18%, Geometric Measurement & Dimensions (G-GMD) 2%–8%, Modeling with Geometry (G-MG) 8%–15%. Algebra II — Number & Quantity 4%–8%, Algebra 30%–39%, Functions 38%–45%, Statistics & Probability 14%–22%.

Official sources

NYSED Grades 3–8 ELA and Math Test Manuals
NYSED Directions for Administering Regents Examinations
NYSED High School Regents Examinations

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Practice playmedium

A survey asked students how many siblings they have. The frequency table shows the responses.
$\begin{array}{c|c} \text{Number of siblings} & \text{Number of students} \\ \hline 0 & 3 \\ 1 & 2 \\ 2 & 4 \\ 3 & 5 \\ 4 & 2 \end{array}$

What is the mean number of siblings per student?

Multiply each sibling count by its frequency and add: $(0 \times 3) + (1 \times 2) + (2 \times 4) + (3 \times 5) + (4 \times 2) = 33$ . With $16$ students, the mean is $\dfrac{33}{16} = 2.0625$ siblings.

Practice playeasy

For two independent events, the probability of flipping two heads in a row: $P(A)=\tfrac{1}{2}$ , $P(B)=\tfrac{1}{2}$ . Find $P(A \text{ and } B)$ as a simplified fraction.

Multiply: $P(A \text{ and } B) = \tfrac{1}{2} \times \tfrac{1}{2} = \tfrac{1}{4}$ .

Practice playeasy

Five students answered the statistical question "How many hours did you sleep last night?" The answers were $9, 4, 11, 6, 2$ . What is the median number of hours?

The median describes the center: put the values in order and take the middle. In order: $2, 4, 6, 9, 11$ . The middle value is $6$ .

Practice playeasy

A student is writing questions about trees. Which of these is a statistical question?

A statistical question anticipates variability: many people or things can give different answers. "How tall are the trees in the park?" asks about many trees, so the heights can differ. It is a statistical question.

Practice playeasy

A biologist measures five plant heights, in inches: $58$ , $60$ , $62$ , $64$ , and $66$ . The tallest plant, $66$ inches, is removed from the data set. How does this affect the mean?

The mean of the original five heights is $\dfrac{58+60+62+64+66}{5}=62$ inches. Because $66>62$ , removing the largest value lowers the mean.

Practice playeasy

The distances, in miles, run on seven days are $6\textsf{,}$ $8\textsf{,}$ $12\textsf{,}$ $9\textsf{,}$ $14\textsf{,}$ $7\textsf{,}$ and $14\textsf{.}$ What is the mean distance?

Mean $= \dfrac{6 + 8 + 12 + 9 + 14 + 7 + 14}{7} = \dfrac{70}{7} = 10$ .

Practice playeasy

Find the median of 3, 7, 9.

Order the data and take the middle value(s): median $= 7$ .

Practice playeasy

Seven test scores are $90\textsf{,}$ $50\textsf{,}$ $80\textsf{,}$ $55\textsf{,}$ $72\textsf{,}$ $60\textsf{,}$ and $83\textsf{.}$ What is the median score?

In order, the values are $50\textsf{,}$ $55\textsf{,}$ $60\textsf{,}$ $72\textsf{,}$ $80\textsf{,}$ $83\textsf{,}$ $90\textsf{.}$ The median is the middle value, $72\textsf{.}$

NY State Math Grades 3–8 Statistics and Probability. Practice it free.

Statistics and Probability skills

Develop understanding of statistical variability

Summarize and describe distributions

Investigate patterns of association in bivariate data

Use random sampling to draw inferences about a population

Investigate chance processes and develop, use, and evaluate probability models

Topics mapped to this domain

Central Measures from Tally Charts (ACT)

Compound probability

Describing a Data Distribution

Identifying Statistical Questions

Mean change from data set edits

Mean from a data list

Measures of center and variability

Median from a data list

One-event probability word problems

Probability basics

Probability from number sets

Probability of simple events

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Turn statistics and probability into game time.

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