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Data Inference and Prediction

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Data Inference and Prediction

Hana and Tui are helping a local food bank plan its weekly deliveries. Use the data to make and evaluate inferences and predictions. Predictions are estimates, not guarantees. Show your reasoning where asked.

Read the evidence

A food bank recorded the number of households served and the number of grocery boxes delivered over six weeks.

Week

Households served

Boxes delivered

100

1.Which statement is an inference supported by these six weeks of data?

Each household receives exactly two boxes every week.
As more households are served, the number of boxes delivered tends to increase.
The food bank will serve exactly 74 households in week 12.
The data proves that no households will need extra food.

2.Describe the association between households served and boxes delivered. Use evidence from at least two rows in the table.

3.The pattern continues for one more week. Predict the number of households served and the number of boxes delivered in week 7. Explain the pattern you used.

4.A volunteer says, “In week 10, exactly 66 households will be served.” Is this a certain fact or a prediction? Give one reason it may not be exact.

Test a prediction

The food bank usually packs 2 boxes per household. Hana checks how many boxes were actually delivered in week 7 and finds that 116 boxes went out for 54 households.

5.Compare the week 7 result with your prediction in Question 3. How many more boxes were delivered than predicted? Give one plausible explanation.

6.Which conclusion is best supported by the first six weeks: “Every household always needs exactly two boxes” or “The food bank delivered two boxes per household in the recorded weeks”? Explain the difference.

7.The team wants to predict demand for a busy holiday week. Name two pieces of extra information that could make the prediction more reliable.

8.The data covers only six ordinary weeks. Which prediction is more trustworthy: estimating demand for next ordinary week, or estimating demand a year from now? Explain.

Next ordinary week, because it is closer to the observed period and conditions are more likely to be similar.
A year from now, because longer predictions are always more accurate.
Both are equally certain because the table has a clear pattern.
Neither can be estimated at all.

9.A post claims, “Food bank demand will double next month.” What two questions would you ask before trusting this prediction?

10.The team has capacity to prepare 120 boxes next week. Based on the six-week pattern, is that likely to be enough? State a prediction and one limitation of your conclusion.