Worksheet

Fitness Tracker: Steps, Alerts, and Associations

Analyze fitness tracker records using two-way frequency tables, relative frequencies, and comparisons that reveal categorical associations.

Grade 8MathInteractive · Printable

Aligned to8.SP.A.4

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Single worksheet
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1 Common Core standard
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14 questions
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Format: Interactive · Printable
Grade: Grade 8
Subject: Math
Question types: Fill in the blank, Multiple choice, Short answer

About this worksheet

What students practice

Students find joint, marginal, and conditional relative frequencies from two-way tables.
Students compare conditional percentages to identify associations between categorical variables.
Students distinguish evidence of association from evidence of cause and effect.

How to use

Have students identify the reference group before calculating each percentage. Discuss why different group sizes make raw counts misleading.

Curriculum

Common Core standard covered

8.SP.A.4

Find patterns of association in categorical data with two-way tables of frequencies and relative frequencies.

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Name Date

Fitness Tracker: Steps, Alerts, and Associations

Use two-way tables to compare categorical tracker records.

Read the Tracker Records

Use the table for Questions 1–5. Each record represents one participant's day. An alert means the tracker recorded a heart rate above that participant's chosen alert setting.

Step Goals and Heart-Rate Alerts
Daily step goal	Alert recorded	No alert	Total
Met	48	32	80
Not met	12	28	40
Total	60	60	120

Which pair of categorical variables does this table compare?

A. The participant's age and the chosen alert setting.
B. Whether the step goal was met and whether an alert was recorded.
C. The exact step count and the exact heart rate.
D. Whether the tracker was charged and whether it was worn.

How many records show both a met step goal and no heart-rate alert? records

What percentage of all 120 records show both a met step goal and a heart-rate alert? %

What percentage of all records show a heart-rate alert, regardless of step-goal status? %

Which calculation gives the percentage of records with an alert among records where the step goal was met?

A. Divide 48 by 60, then multiply by 100.
B. Divide 48 by 120, then multiply by 100.
C. Divide 80 by 120, then multiply by 100.
D. Divide 48 by 80, then multiply by 100.

Compare Within Groups

Continue using the Step Goals and Heart-Rate Alerts table. For each conditional percentage, use the total for the group named in the question.

Among records where the step goal was met, what percentage show an alert? %
Among records where the step goal was not met, what percentage show an alert? %

Subtract the alert percentage for the goal-not-met group from the alert percentage for the goal-met group. What is the difference? percentage points

Among the 60 records with an alert, what percentage show a met step goal? %

Which conclusion best describes the association in these records?

A. Alerts were equally common in both groups: 50% versus 50%.
B. Alerts occurred on every record in the goal-met group: 100% versus 30%.
C. Alerts were more common in the goal-met group: 60% versus 30%.
D. Alerts were less common in the goal-met group: 30% versus 60%.

Test New Tracker Claims

Use the new table in each question or question group. Compare percentages within the appropriate groups, not just counts.

10.

A second tracker study recorded the following counts.

Second Study
Daily step goal	Alert recorded	No alert	Total
Met	20	30	50
Not met	40	60	100
Total	60	90	150

Complete the row-relative percentages for the goal-not-met group.
Alert recorded: %; no alert: %

11.

Use the Second Study table. Twice as many alerts occurred in the goal-not-met group as in the goal-met group. Which interpretation is supported?

A. The groups had the same alert rate: 40% in each group.
B. The goal-met group had the higher alert rate: 60% versus 40%.
C. The goal-not-met group had twice the alert rate: 80% versus 40%.
D. The groups had the same alert rate: 60% in each group.

12.

A tracker team grouped records by day type. In which group was a heart-rate alert more common?

Alerts by Day Type
Day type	Alert recorded	No alert	Total
Weekday	24	56	80
Weekend	18	22	40

A. Weekend records had the higher rate: 45% versus 30%.
B. Both groups had the same rate: 35% in each group.
C. Weekday records had the higher rate: 70% versus 55%.
D. Weekday records had the higher rate: 24% versus 18%.

13.

A third study reports row-relative frequencies instead of counts. It includes 60 records in which the step goal was met.

Third Study: Percent Within Each Row
Daily step goal	Alert recorded	No alert	Total
Met	65%	35%	100%
Not met	45%	55%	100%

How many of the 60 goal-met records show an alert? records

14.

Use the Third Study table. Jordan says, “The percentages prove that meeting a step goal causes a heart-rate alert.” Explain what the percentages do show and why Jordan's causal claim is not justified.