IAR Grades 6-8 Statistics and Probability. Practice it free.

Develop understanding of statistical variability and summarize and describe distributions. This Grades 6-8 reporting domain maps to 9 practice skills and 8 representative questions from the playable bank.

Grades 6-89 mapped skills
What the test measures

Statistics and Probability skills

  1. develop understanding of statistical variability

  2. summarize and describe distributions

  3. investigate patterns of association in bivariate data

Standards basis

Illinois Learning Standards incorporating the Common Core State Standards (CCSS-M) — Illinois

How the IAR reports it

IAR is Illinois’ state assessment built on the Illinois Learning Standards incorporating the Common Core, and its math design follows the PARCC-style blueprinting approach used for grades 3–8. ISBE’s resources page points to the PARCC mathematics model content frameworks, and the IAR page says the math evidence statements are aligned directly to the Common Core State Standards.

Blueprint & weighting

IAR uses the PARCC-derived / Illinois Assessment of Readiness (IAR) framework (by grade domains structure).

Try it now

8 free questions · 0/0 correct

Practice playmedium

A fitness tracker recorded daily step counts, in thousands of steps, over 1414 days. The frequency table shows the results.
Steps (thousands)Number of days5382114143172\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: (5×3)+(8×2)+(11×4)+(14×3)+(17×2)=151(5 \times 3) + (8 \times 2) + (11 \times 4) + (14 \times 3) + (17 \times 2) = 151. With 1414 days, the mean is 1511410.79\dfrac{151}{14} \approx 10.79 thousand steps.

Practice playeasy

Students answered the statistical question "How many snacks did you pack?" The data are 3,5,7,133, 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=283 + 5 + 7 + 13 = 28, and 28÷4=728 \div 4 = 7.

Practice playeasy

Mia writes three survey questions:

• How many minutes do students in my class spend on homework?
• How many minutes did I spend on homework last night?
• How tall are the players on my team?

How many of the three are statistical questions?

A statistical question anticipates variability. Asking how many minutes students spend on homework, and how tall the players are, both ask about a group, so the answers can differ. Asking how many minutes I spent last night asks about one person on one night, so it has one answer. That makes 22 statistical questions.

Practice playeasy

A bookstore tracks five daily sales totals, in dollars: 1010, 1515, 2020, 2525, and 3030. A sixth day with sales of 2020 is added to the data set. How does this affect the mean?

The mean of the original five totals is 10+15+20+25+305=20\dfrac{10+15+20+25+30}{5}=20 dollars. Because the new value equals the current mean, the mean stays 2020.

Practice playeasy

Five afternoon temperatures, in degrees Fahrenheit, are 68,68\textsf{,} 72,72\textsf{,} 65,65\textsf{,} 74,74\textsf{,} and 71.71\textsf{.} What is the mean temperature?

Mean =68+72+65+74+715=3505=70= \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 44 appears twice, so the mode is 44.

Practice playeasy

Seven morning temperatures, in degrees Fahrenheit, are 58,58\textsf{,} 80,80\textsf{,} 70,70\textsf{,} 62,62\textsf{,} 72,72\textsf{,} 64,64\textsf{,} and 56.56\textsf{.} What is the median temperature?

In order, the values are 56,56\textsf{,} 58,58\textsf{,} 62,62\textsf{,} 64,64\textsf{,} 70,70\textsf{,} 72,72\textsf{,} 80.80\textsf{.} The median is the middle value, 64.64\textsf{.}

Practice playeasy

A line of best fit for the number of lawns Jaden mows xx and his savings yy in dollars is y=15x+40y = 15x + 40. According to the line, how many dollars did Jaden have saved before mowing any lawns?

At x=0x = 0 lawns, y=40y = 40: the yy-intercept is the starting savings.

Keep practicing

Turn statistics and probability into game time.

The IAR placement starts with this test's real coverage map and finds the right difficulty.