NDSA Grade 6 Statistics and Probability Practice

Statistics and Probability skills

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Summarize numerical data sets in relation to their context, such as reporting center and variability.

Standards basis

North Dakota State Content Standards for Mathematics — North Dakota

How the NDSA reports it

North Dakota administered its own state assessment program (the NDSA, a Cambium computer-adaptive test in grades 3-8 and 10; replaced by ND A+ beginning spring 2025). An official NDSA mathematics public-facing CAT blueprint (Cambium/NDDPI, Oct 2020) does exist and lists per-grade reporting categories with percentage ranges, but its full per-grade table could not be retrieved character-for-character from a citable primary source for transcription here (the Cambium content CDN blocks programmatic access). The NDSA reporting categories are the CCSS-M grade-level domains: the assessment was built on North Dakota's 2017 math standards, which are verbatim CCSS-M organized by grade-level domains. The coverage map below uses North Dakota's 2023-standards-style domain/standard codes (e.g. 3.AR.OA) but the skill content is CCSS-M.

Blueprint & weighting

An official NDSA mathematics CAT blueprint (Cambium/NDDPI public-facing CAT version, Oct 2020) publishes per-grade reporting-category percentage ranges (e.g. grade 3 Operations and Algebraic Thinking ~31-34%, Number and Operations in Base Ten ~22-24%; grade 6 groups Ratios & Proportional Relationships and The Number System ~28-34% and Expressions and Equations ~25-29%). The complete per-grade table could not be retrieved verbatim from a citable primary source (the Cambium content CDN returns HTTP 403 to programmatic fetches), so domain weights in the mapping are left null rather than transcribing partial/uncertain figures or splitting blueprint percentages across the grade-6+ domain groupings.

Official sources

North Dakota DPI – State Assessment page
North Dakota DPI – Home
North Dakota Department of Agriculture – Ag Mag teacher guide with ND math standards references

8 free questions · 0/0 correct

Practice playmedium

A fitness tracker recorded daily step counts, in thousands of steps, over $14$ days. The frequency table shows the results.
$\begin{array}{c|c} \text{Steps (thousands)} & \text{Number of days} \\ \hline 5 & 3 \\ 8 & 2 \\ 11 & 4 \\ 14 & 3 \\ 17 & 2 \end{array}$

What is the mean step count per day?

Multiply each step count by its frequency and add: $(5 \times 3) + (8 \times 2) + (11 \times 4) + (14 \times 3) + (17 \times 2) = 151$ . With $14$ days, the mean is $\dfrac{151}{14} \approx 10.79$ thousand steps.

Practice playeasy

Students answered the statistical question "How many snacks did you pack?" The data are $3, 5, 7, 13$ . What is the mean of the data?

The mean describes the center: add the values and divide by how many there are. $3 + 5 + 7 + 13 = 28$ , and $28 \div 4 = 7$ .

Practice playeasy

Jaden lists four questions:

• What is my dog's weight?
• How much do the dogs at the animal shelter weigh?
• How old is my teacher?
• How tall is my desk?

How many of the four are statistical questions?

A statistical question anticipates variability. Asking how much the dogs at the animal shelter weigh asks about a group, so the weights can differ. Asking about one dog, one teacher, or one desk has a single answer. That makes $1$ statistical question.

Practice playeasy

A bookstore tracks five daily sales totals, in dollars: $10$ , $15$ , $20$ , $25$ , and $30$ . A sixth day with sales of $20$ is added to the data set. How does this affect the mean?

The mean of the original five totals is $\dfrac{10+15+20+25+30}{5}=20$ dollars. Because the new value equals the current mean, the mean stays $20$ .

Practice playeasy

Five afternoon temperatures, in degrees Fahrenheit, are $68\textsf{,}$ $72\textsf{,}$ $65\textsf{,}$ $74\textsf{,}$ and $71\textsf{.}$ What is the mean temperature?

Mean $= \dfrac{68 + 72 + 65 + 74 + 71}{5} = \dfrac{350}{5} = 70$ .

Practice playeasy

Find the mode of the data set 4, 4, 7, 9, 10, 11.

The mode is the value that appears most often. Only $4$ appears twice, so the mode is $4$ .

Practice playeasy

Seven morning temperatures, in degrees Fahrenheit, are $58\textsf{,}$ $80\textsf{,}$ $70\textsf{,}$ $62\textsf{,}$ $72\textsf{,}$ $64\textsf{,}$ and $56\textsf{.}$ What is the median temperature?

In order, the values are $56\textsf{,}$ $58\textsf{,}$ $62\textsf{,}$ $64\textsf{,}$ $70\textsf{,}$ $72\textsf{,}$ $80\textsf{.}$ The median is the middle value, $64\textsf{.}$

Practice playmedium

A basketball player recorded points scored in each of $16$ games. The frequency table shows the results.
$\begin{array}{c|c} \text{Points scored} & \text{Number of games} \\ \hline 18 & 2 \\ 21 & 3 \\ 24 & 4 \\ 27 & 4 \\ 30 & 3 \end{array}$

What is the mean number of points scored per game?

Multiply each point total by its frequency and add: $(18 \times 2) + (21 \times 3) + (24 \times 4) + (27 \times 4) + (30 \times 3) = 393$ . With $16$ games, the mean is $\dfrac{393}{16} = 24.5625$ points per game.