CMAS High school Statistics & Probability Practice

Statistics & Probability skills

Summarize, represent, and interpret data on a single count or measurement variable

Summarize, represent, and interpret data on two categorical and quantitative variables

Make inferences and justify conclusions from sample surveys, experiments, and observational studies

Understand and evaluate random processes underlying statistical experiments

Use the rules of probability to compute probabilities of compound events in a uniform probability model

Standards basis

Colorado Academic Standards (mathematics) — Colorado

How the CMAS reports it

CMAS is Colorado’s statewide summative assessment system aligned to the Colorado Academic Standards rather than a national framework like SBAC or NAEP. The official CMAS page and Colorado standards materials indicate the math assessment is built from Colorado Academic Standards, but the retrieved official CMAS page did not expose a separate math blueprint document.

Blueprint & weighting

No official CMAS math domain weighting/percent-of-items blueprint was available in the retrieved primary CMAS materials.

Official sources

Colorado Department of Education CMAS page
Colorado Department of Education Colorado Academic Standards and Essential Skills page

8 free questions · 0/0 correct

Practice playeasy

A class has $6$ students, and $3$ will be chosen for a group. What is $C(6, 3)\textsf{?}$

$C(6,3) = \dfrac{6!}{3! \cdot 3!} = \dfrac{720}{6 \cdot 6} = 20\textsf{.}$

Practice playeasy

A fair lists $8$ booths, and a student will visit a first booth and then a second booth. What is $P(8, 2)\textsf{?}$

$P(8,2) = \dfrac{8!}{6!} = \dfrac{40320}{720} = 56\textsf{.}$

Practice playeasy

Four data sets show the number of laps run in five trials. Which set has the least standard deviation?

Set A: $2, 4, 6, 8, 10$
Set B: $5, 5, 6, 6, 8$
Set C: $1, 5, 6, 7, 11$
Set D: $3, 5, 6, 7, 9$

Set B has mean $6$ with repeated values near the center ( $5, 5, 6, 6, 8$ ), giving the smallest standard deviation, about $1.1$ . The other sets include values farther from their means.

Practice playeasy

Five afternoon temperatures, in degrees Fahrenheit, are $68\textsf{,}$ $72\textsf{,}$ $65\textsf{,}$ $74\textsf{,}$ and $71\textsf{.}$ Which data set has the same mean?

The original mean is $\dfrac{68 + 72 + 65 + 74 + 71}{5} = 70$ . The set $66\textsf{,}$ $68\textsf{,}$ $70\textsf{,}$ $72\textsf{,}$ $74$ also has mean $70$ , so the means match.

Practice playeasy

The distances, in miles, run on seven days are $14\textsf{,}$ $6\textsf{,}$ $20\textsf{,}$ $9\textsf{,}$ $11\textsf{,}$ $18\textsf{,}$ and $6\textsf{.}$ Which data set has the same median?

In order, the original values have middle value $11$ , so the median is $11$ . The set $4\textsf{,}$ $5\textsf{,}$ $8\textsf{,}$ $11\textsf{,}$ $22\textsf{,}$ $25\textsf{,}$ $28$ also has median $11$ , so the medians match.

Practice playeasy

What is $1!\textsf{?}$

$1! = 1\textsf{.}$

Practice playeasy

In three bowling games, Alex rolled scores of $142$ , $156$ , and $138$ . In a fourth game, the score was $x$ . The mean score over the four games is $150$ . What is the value of $x$ ?

Four games with a mean of $150$ total $4 \times 150 = 600$ . Since $142 + 156 + 138 = 436$ , $x = 600 - 436 = 164$ .

Practice playeasy

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

The minimum of the data is $2$ .

CMAS High school Statistics & Probability. Practice it free.

Statistics & Probability skills

Summarize, represent, and interpret data on a single count or measurement variable

Summarize, represent, and interpret data on two categorical and quantitative variables

Make inferences and justify conclusions from sample surveys, experiments, and observational studies

Understand and evaluate random processes underlying statistical experiments

Use the rules of probability to compute probabilities of compound events in a uniform probability model

Topics mapped to this domain

Calculating combinations (ACT)

Calculating permutations (ACT)

Compare standard deviation of data sets (ACT)

Comparing means

Comparing medians

Factorials (ACT)

Find score from mean

Interpreting data displays

Normal distribution basics

Problem solving in context (SAT)

Statistics basics

Two-event conditional probability word problems (SAT)

8 free questions · 0/0 correct

Turn statistics & probability into game time.

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