Central Measures from Tally Charts (ACT). Game on.

Central Measures from Tally Charts (ACT) is a grade 6 math skill aligned to Common Core standard 6.SP.B.5.c. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 central measures from tally charts (act) problems our math games drill.

CCSS 6.SP.B.5.c10 questions in the bank
Kickoff

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Warm-upeasy

The table shows quiz scores and how many students earned each score.
Quiz scoreNumber of students622683745803863\begin{array}{c|c} \text{Quiz score} & \text{Number of students} \\ \hline 62 & 2 \\ 68 & 3 \\ 74 & 5 \\ 80 & 3 \\ 86 & 3 \end{array}

What is the median quiz score?

There are 1616 scores. Listing every score from least to greatest, the 88th and 99th values are both 7474, so the median is 7474.

Mid-gameeasy

A student tracked minutes spent studying each night for 1616 nights. The frequency table shows the results.
Minutes studiedNumber of nights102204303405502\begin{array}{c|c} \text{Minutes studied} & \text{Number of nights} \\ \hline 10 & 2 \\ 20 & 4 \\ 30 & 3 \\ 40 & 5 \\ 50 & 2 \end{array}

What is the median number of minutes studied per night?

Expand to 1616 values: 10,10,20,20,20,20,30,30,30,40,40,40,40,40,50,5010, 10, 20, 20, 20, 20, 30, 30, 30, 40, 40, 40, 40, 40, 50, 50. The 88th and 99th values are both 3030, so the median is 3030 minutes.

Mid-gameeasy

A shipping clerk weighed 1414 packages. The frequency table shows each weight and how many packages had that weight.
Weight (lb)Number of packages2372125172222\begin{array}{c|c} \text{Weight (lb)} & \text{Number of packages} \\ \hline 2 & 3 \\ 7 & 2 \\ 12 & 5 \\ 17 & 2 \\ 22 & 2 \end{array}

What is the median package weight?

There are 1414 weights. Listing every weight from least to greatest, the 77th and 88th values are both 1212, so the median is 1212 pounds.

Mid-gameeasy

A clinic recorded customer wait times, in minutes, for 1616 visits. The frequency table shows the results.
Wait time (min)Number of customers225382116143\begin{array}{c|c} \text{Wait time (min)} & \text{Number of customers} \\ \hline 2 & 2 \\ 5 & 3 \\ 8 & 2 \\ 11 & 6 \\ 14 & 3 \end{array}

What is the median wait time?

Expand to 1616 wait times: 2,2,5,5,5,8,8,11,11,11,11,11,11,14,14,142, 2, 5, 5, 5, 8, 8, 11, 11, 11, 11, 11, 11, 14, 14, 14. The 88th and 99th values are both 1111, so the median is 1111 minutes.

Mid-gamemedium

A coach recorded how many goals the team scored in each of 1616 games. The frequency table shows the results.
Goals scoredNumber of games1234547393\begin{array}{c|c} \text{Goals scored} & \text{Number of games} \\ \hline 1 & 2 \\ 3 & 4 \\ 5 & 4 \\ 7 & 3 \\ 9 & 3 \end{array}

What is the mean number of goals scored per game?

Multiply each goal total by its frequency and add: (1×2)+(3×4)+(5×4)+(7×3)+(9×3)=82(1 \times 2) + (3 \times 4) + (5 \times 4) + (7 \times 3) + (9 \times 3) = 82. With 1616 games, the mean is 8216=5.125\dfrac{82}{16} = 5.125 goals per game.

Mid-gamemedium

A survey asked students how many siblings they have. The frequency table shows the responses.
Number of siblingsNumber of students0312243542\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: (0×3)+(1×2)+(2×4)+(3×5)+(4×2)=33(0 \times 3) + (1 \times 2) + (2 \times 4) + (3 \times 5) + (4 \times 2) = 33. With 1616 students, the mean is 3316=2.0625\dfrac{33}{16} = 2.0625 siblings.

Mid-gamemedium

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 15114≈10.79\dfrac{151}{14} \approx 10.79 thousand steps.

Buzzer beatermedium

A basketball player recorded points scored in each of 1616 games. The frequency table shows the results.
Points scoredNumber of games182213244274303\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: (18×2)+(21×3)+(24×4)+(27×4)+(30×3)=393(18 \times 2) + (21 \times 3) + (24 \times 4) + (27 \times 4) + (30 \times 3) = 393. With 1616 games, the mean is 39316=24.5625\dfrac{393}{16} = 24.5625 points per game.

Overtime

2 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

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Tests that cover central measures from tally charts (act):
ACTSBACNAEPSC READYVTCAP
Reporting domains for this skill
SAT All grades: Problem-Solving and Data AnalysisACT All grades: Integrating Essential SkillsACT All grades: Preparing for Higher MathSTAAR Grade 6: Data Analysis, Personal Financial Literacy, and ProbabilitySTAAR Grade 7: Data Analysis, Personal Financial Literacy, and ProbabilityMAP Growth Math 6+: Statistics and Probability
More Grade 6 skills
Absolute valueArea formulas (triangle, parallelogram, trapezoid)Combining like termsCustom unit conversionsCombining like terms and distributingDecimal operationsDescribing a Data DistributionFraction-decimal-percent conversionAll Grade 6 practice →

Drill it inside a game.

The free placement test finds your level, then every match serves central measures from tally charts (act) questions at exactly the right difficulty.