IB Mathematics Applications & Interpretation Question Type 1: Given Some Worded Scenario of Real-life Data Collection, Outlining the Characteristics of the Data and Possible Problems Exercises

In a stratified sample, $30\%$ of customers are female and $70\%$ are male. You plan to sample $200$ customers in total. Calculate the number of females and the number of males to include in the sample.

In a study of the number of plates of food consumed by restaurant customers at lunchtime, define the population and the sample.

Explain why collecting female data in the morning and male data at night can affect the validity of conclusions about gender differences. [3 marks]

Find the overall average number of plates consumed across all $100$ customers.

A restaurant surveys the first 30 customers arriving between 12 pm and 1 pm. Name the sampling technique used.

In a survey of food consumption, data from females were collected in the morning and data from males were collected at night.

Identify one major source of bias in this study.

A survey asks customers “How satisfied are you with your meal?” on a scale from $1$ (very unsatisfied) to $5$ (very satisfied). Identify the variable type and its measurement level.

Design a stratified sampling method to study the number of plates consumed, using gender to define the strata. Describe the steps involved.

A sample of 40 female customers had an average of 4.2 plates and a sample of 60 male customers had an average of 3.6 plates. Calculate the absolute difference and the percentage difference (relative to the male average).

Classify the variable “amount spent on food” in dollars and cents in terms of type and level of measurement.

Suggest one method to reduce response bias when collecting customers’ self-reported number of plates consumed.

The variable "number of plates consumed" was recorded for each sampled customer. State the type and level of this variable.