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Multivariate Data Investigation Worksheet

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Multivariate Data Investigation Worksheet

A food bank team is exploring how volunteer shifts work. Read the data table, look for patterns between variables, and answer the questions. A relationship in data does not by itself prove that one variable causes another.

The investigation

The team recorded information from 10 volunteer shifts. Shift length is measured in hours; parcels packed is the number completed during that shift. The role column records the main task for that shift.

Shift length (hours)

Parcels packed

Main role

Packing

Sorting

Packing

Sorting

Packing

Sorting

Explore and interpret

Use evidence from the table in your answers. A multivariate investigation considers several variables together.

1.Which is the strongest investigative question for these data?

How many parcels were packed in the 3-hour shifts?
Is there a relationship between shift length, main role, and the number of parcels packed?
Which volunteer is the best?
Does every shift pack exactly 20 parcels?

2.Identify the population the team would need to study if it wanted to make a claim about all food bank shifts, rather than just the 10 recorded shifts.

3.Write one reasonable conjecture about the relationship between shift length and parcels packed. Support it with two examples from the table.

4.Which is a categorical variable in the table, and which two are numerical variables?

5.Compare the packing shifts with the sorting shifts. Find the mean number of parcels for each group and state one limitation of this comparison.

6.Which graph would best show the relationship between shift length and parcels packed, and what would go on each axis?

7.The 2-hour shifts packed 16, 18, and 12 parcels. Describe the pattern within this group and give one possible reason for the difference.

8.A team member says, “Longer shifts cause volunteers to pack more parcels.” Is that conclusion justified by this table? Explain the difference between association and causation.

9.The team wants to collect more data. Choose the fairest plan: A) record every shift for one week and note shift length, role, and parcels packed; B) record only the busiest packing shifts; C) ask one volunteer to estimate the usual totals. Explain your choice.

10.Suggest one ethical step the food bank should take before collecting or sharing shift data, and explain why it matters.