Topic 4.1: Types of Data and Sampling Questions

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.

Calculate the mean of the dataset 4, 5, 6, 7, 8, 50. Then recalculate without the 50. Comment on the difference.

A dataset has Q1 = 12, Q3 = 28. Calculate the IQR and find the lower and upper outlier bounds.

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

State two statistics that are RESISTANT to outliers and two that are HIGHLY AFFECTED by outliers.

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

A journalist surveys ''public opinion'' by stopping people in a wealthy shopping district at 11 am on a Wednesday. State two sources of bias.

A list of 600 items needs a systematic sample. The first item selected is item number 7, and the interval k = 12. Find the second and third items selected.

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

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

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

A hospital department has 240 staff: 60 doctors, 120 nurses, 60 admin. The total sample = 40 stratified by role. Calculate the number of each.

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.

State one advantage of stratified sampling over simple random sampling.

A library has 800 members. The librarian wants a systematic sample of 40 members. Find the sampling interval k.

A school has 600 students: 240 in Year 11 and 360 in Year 12. A stratified sample of 50 is taken. How many students from each year should be selected?

A city council wants to know if residents support a new park. They survey 500 people who pass a particular bus stop. Identify (i) the population (ii) the sample.

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?

A dataset has Q1 = 8, median = 12, Q3 = 16. A new value of 30 is added. Is it an outlier?