Topic 4.1: Types of Data and Sampling Questions

Repeated weighings of the same object give 102.1, 101.9, 102.0, 102.2, 101.8 grams. Identify the error type.

Given Q1 = 50 and IQR = 20, the lower outlier bound is:

Classify each variable as qualitative, discrete quantitative, or continuous quantitative: (a) eye colour, (b) number of cars in a car park, (c) weight of a parcel in kg.

An ecologist studies the population of frogs in a national park. She captures 80 frogs from a specific pond. State the population and the sample.

A health survey of 30 people aims to estimate the average blood pressure of all adults in a country. Comment on the sample size.

State the data type for each: (a) student''s favourite subject, (b) goals scored in a match, (c) time to complete a race in seconds.

A school nurse is planning a study on student wellbeing. For each student she will record: the number of hours of sleep, the favourite type of exercise, the resting heart rate, and the year group.

A company has 480 employees: 120 managers, 240 office staff, 120 factory workers. A stratified sample of 40 is taken. How many from each group?

A factory list of 2400 components needs a systematic sample of 80. (a) Find the sampling interval k. (b) If the random start is 17, list the first three components selected.

A questionnaire asks: ''Do you agree that the school''s policy on phones is too strict?'' Identify and explain the bias.

A research project asks: ''Do you agree that the government''s wasteful spending policies should be reduced?'' Identify the issue.

A biologist tags 200 fish in a lake and later catches another 150 fish, of which 8 are tagged. The biologist wants to estimate the total fish population. What is the population in this study?

In a stratified sample of size n drawn from a population of size N split into strata of sizes n₁, n₂, …, the number sampled from stratum i is given by (nᵢ/N) × n. A population has strata 100, 200, 300. A sample of 30 is needed. Find the size from each.

Given Q1 = 20, Q3 = 32, identify which of the following are outliers: 5, 15, 35, 55, 60.

A survey records, for each student, their shoe size, their height in centimetres, their eye colour and the number of siblings they have. Classify each variable as qualitative, discrete numerical or continuous numerical.

A factory has 320 workers in three shifts: morning (160), afternoon (96), night (64). A stratified sample of 40 workers is taken. State the number of workers selected from each shift.

A company has 1500 employees. Quality control wants to interview 75 employees systematically. State the sampling interval and explain how the start is chosen.

A factory produces 50 000 light bulbs per day. The quality control team tests 200 bulbs randomly chosen from the daily output. Identify the population and the sample.

A thermometer reads 1°C higher than the true temperature, every time. State the type of error and one way to correct it.

A school has 600 students: 360 girls and 240 boys. The head teacher wants a sample of 50 students whose proportions of girls and boys match the whole school. State the name of this sampling method, and find how many girls and how many boys should be in the sample.