MAST Grade 6 Concepts of Statistics Practice

Concepts of Statistics skills

Recognize statistical questions and display numerical data on a number line.

Summarize data sets in relation to their context.

Standards: 6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5, 6.SP.5.a, 6.SP.5.b, 6.SP.5.c, 6.SP.5.d

Standards basis

Montana PK-12 Mathematics Content Standards / Common Core State Standards for Mathematics (CCSS-M)-aligned Montana standards — Montana

How the MAST reports it

Montana’s MAST is a state-specific through-year assessment built by New Meridian and aligned to Montana’s academic content standards, not a Smarter Balanced-style claims/targets framework. The math blueprints organize content into grade-level strands/testlets that map directly to CCSS-M-derived Montana standards.

Blueprint & weighting

The blueprint publishes a through-year design of 12 strands/testlets per grade, with 1 strand per testlet, 2 reporting attributes per strand, and 9–13 items per testlet. It also specifies approximate item-type and DOK distributions, but does not publish percentage weighting by domain in the captured blueprint text.

Official sources

Montana OPI MontCAS
Montana OPI - MasteryGuide Mathematics Assessment Specifications and Blueprints
Montana OPI - Montana MAST Math Testlets

8 free questions · 0/0 correct

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

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

Coach Rivera brainstorms four questions:

• How many push-ups can each player on my team do?
• How many push-ups did the team captain do today?
• How many sit-ups can each player on my team do?
• How many laps can each player on my team run?

How many of the four are statistical questions?

A statistical question anticipates variability. Asking how many push-ups, sit-ups, or laps each player can do asks about every player, so the answers can differ from player to player. Asking how many push-ups the team captain did today asks about one person on one day, so it has one answer. That makes $3$ statistical questions.

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, $72\textsf{.}$

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.